Index to be hyperlinked as finished
General Concepts (this post)
General Character Building Guidelines
Building a Wizard
-The Blast Mage
-The Bleed Mage
-The Master of Puppets
-The Master of Space
Multi-Classing into Wizards
-The Master of Time
-The Dark Lord of the Sith
-The Binder of Blood
Treantmonk's guide to Wizards: God 4e style Good stuff from another wizard enthusiast with a slightly different perspective
Gish Handbook currently lacking in content, but may eventually be helpful
Seeker of Truth's list of ways for a wizard to get Combat Advantage
McDungeon's Elf Illusionist mini-Guide
To light a candle is to cast a shadow. - Ursula K. Le Guin, A Wizard of Earthsea
There are multiple ways to approach building an arcane-inclined character. A straight-class character has two real options at present, and multi-classing introduces additional possibilities.
Pure wizard characters will tend towards either blasting or control. In fact, there are fairly important differences between the two options that makes focusing on both almost impossible. But unlike in former editions, control mages will also deal damage simultaneously, while blast mages will also end up having some control. But their goals differ markedly, and thus they will make different choices in powers known, prepared, and options chosen.
Wizards can also multiclass into other classes and other classes can multi-class into arcane power. This creates a dizzying array of possibilities to be explored.
A note about organization: mage types are categorized by build goals rather than similarities of attribute demands or similar concerns, in part because most people are going to start off by saying "i want to blow stuff up with my mind" or "i want to keep the enemy from doing stuff", not "I want an int/wis build wizard, what are my options?". In general, most blast wizards will have similar builds, and most control wizards will have similar builds, and when a particular style wants to build like the other concept type it will direct you there for the relevant pieces of advice. This should make it easier to quickly find the information you are looking for.
A Blast Mage focuses on dealing damage. While a wizard is generally outclassed by striker role classes at single-target damage, no one surpasses the wizard at room-clearing capability, and so a wizard who wants to lay down the hurt is concerned about dealing as much damage as possible per attack and hitting as many targets as possible. The ultimate goal of a Blast Mage is to maximize their DPS (damage per "second"), which means not only choosing high damage spells but also taking options and building their character to maximize their to-hit chances.
A Bleed Mage will try to maximize their DPS to a single target by applying spells which produce ongoing damage and layering these on a single target. These wizards will still want some good AoE damage spells, and still care about total damage output, but have focused more effort into dealing to one target and AoE spells are a secondary concern. They may alternately splash a control focus. They tend to build more like control mages than typical blast mages, but are more interested in DPS optimization than control mages. (Meme name subject to change. Referred to as (hybrid) throughout the document until a permanent name is arrived at.)
A Control Mage focuses on disabling or otherwise disadvantaging their opponents to make it easier for team hero to beat team monster. While area damage is of some importance (as clearing out minion monsters does exert control), they are generally far more interested in spells which produce status effects, and maintaining those status effects for as long as possible.
A Hard Control approach focuses on status conditions tied to monsters which give the monster no choice about how much it effects them. Any spell which produces an effect tied to a monster is a hard control spell. Additionally, barriers which cannot be crossed are hard control - the monster can't opt to go through it. (A barrier like Wall of Ice also arguably qualifies because it takes enough effort to breach to make it effectively impassable for a short time).
A Soft Control approach focuses on discouraging monsters from taking certain actions by making it painful or difficult to do so. Area of effect spells which produce ongoing damage fields or create difficult terrain fall into this category, including spells like Icy Terrain and Wall of Fire.
Spells which move an enemy are somewhere in the boundary between hard and soft control, depending on how easy it is to undo the effect. So thunderwave is more Soft Control because the monster can just move back to undo it pretty trivially most of the time. Something which knocks the monster prone is harder to undo and is more in the middle because standing up takes an action.
A control mage will typically use some spells of both types, although specialization in one or the other is possible.
The first goal in building any wizard is to optimize its abilities for the offensive role chosen. This starts with attributes, and proceeds through class options, power selection, and feat selection. Even skills are important here.
The second goal is in enhancing your wizard's defensive capabilities. 4E by its very nature is structured to keep everyone on the RNG, which means your defenses are both important and definitely matter against level appropriate monsters. As most feats will not help you with role fulfillment, a lot of feats can and should be spent on defensive abilities. Utility powers can also come in handy here.
Finally, general utility is important to a wizard. Some feats can be spared here, but also utility powers and rituals contribute to your suite of options. Skills can be useful, but as most of your in-class options are knowledges, skills only contribute to utility insofar as knowledges do most of the time.
General Character Building Guidelines
One of the major changes in 4E is that your attributes are the most important determiner of how well you accomplish various tasks. Due to the rate at which monster defenses scale, this means that an attack attribute modifier less than +3 is basically worthless, and you better keep investing in improving it or you will quickly fall behind. This also means that generally you'll have one good attack attribute. Fortunately, wizards only have one such attribute - intelligence - unless you want to use a melee or ranged weapon (not recommended for pure wizards).
The other major change is the division of attributes into three groups: the fortitude group (str and con), the reflex group (int and dex), and the will group (wis and cha). Generally you'll want to have one good number in each of those groups and can sack the other one, barring specific other needs (feat prereqs, important attributes, etc...).
All wizards want a good intelligence, as that is the primary stat for many wizard skills and their attack attribute. It should be at least 16 to start, and all attribute pumps you gain should pump intelligence as one of your choices.
Wizards will also want to ensure they have a good secondary attribute, generally either dexterity or wisdom. In general, blast mages are interested in dexterity because of wand focus, while control mages are interested in wisdom because of orb focus. This means most control mages have a better attribute build in general because wisdom and intelligence contribute differently to defense (whereas most of dexterity's possible contributions are duplicated by intelligence). The bleed mage will also want orb focus, and thus a high wisdom. This secondary attribute should also be pumped at every opportunity. It is possible this 'secondary' attribute will actually be more important than intelligence, and this will be discussed under the builds themselves.
The last facet to look at is feats. Most control and all bleed mages will want Spell Focus in the paragon tier, and will thus need cha 13 to qualify. As you'll get +1 to all attributes before choosing the feat, this means a 12 Cha - an attribute which is otherwise wasted. Barring a critical feat like that, because of the sparsity of points to spend on attributes it is strongly recommended to not go out of the way investing in useless attributes. Thus Arcane Reach, while potentially useful for control mages, is also prohibitively inaccessible with a 15 dex requirement (and as its not critical, should be avoided), whereas a blast mage could easily snag this feat.
After you've made sure you qualify for any and all feats you'll need, constitution makes the best investment for fortitude defense as strength is not especially useful to you. Similarly, if you don't have will defense covered yet, wisdom is generally the better investment because it applies to a number of important skills (such as Nature and Insight). However, wizards looking to multiclass could choose the other attribute within pairs at this point to facilitate their desired multiclass.
It is also possible to build a wizard with no real secondary attribute, generally by staff focus. However, as wand and orb are far better foci for your offensive capabilities (blast and control respectively), focusing on staff to avoid those particular secondary attributes is only likely if you need a good attribute elsewhere for multiclassing.
In addition to the more specific advice given later on for power selection relative to your offensive specialty, a general aspect to keep in mind is that one of the strengths of the wizard class is its ability to target any of reflex, fortitude, or will. As such, making sure you have a spell capable of hitting any of those is generally to your advantage, because you can choose the power your adversary is most vulnerable to (ie, has the weakest defense against).
All wizards receive the four cantrips at 1st level. These are remarkably useful and useable at-will.
Mage Hand is a conjuration effect, and can exert ~20lbs of force. Potentially quite useful (Pull levers, carry treasure, etc...).
Prestidigitation has a number of useful facets for minor things.
Light means you don't have to hold a torch in your hands.
Ghost Sound could be quite good for distraction in pre-combat settings, although a wizard's general lack of stealth doesn't facilitate this well.
As usual, cantrips utility is based on your creativity and your groups willingness to ad hoc occasionally.
At first level you get to focus your practice on the use of a particular implement.
Orb is by far the best if you intend to create ongoing conditions which your opponent will need to save against, and demands a high wisdom modifier to be effective. This means most control wizards and (hybrid) wizards will want to focus on orbs. It also means that wisdom is actually more important to them than intelligence, and thus will tend to spend points equally (in a PB setting) between the two of them, and choose a race with a wisdom pump. This is discussed in more detail under Control Mages.
Wand is the best for Blast Mages because it gives them a useful bonus to hit 1/encounter, letting the ramp up their DPS briefly.
Staves have a defensive power, and will likely see more use for wizards heading towards multi-classing, or as a second implement with the appropriate paragon tier feat.
Most wizards, with or without Second Implement, will likely consider holding an implement in each hand. Only those who choose Wand of Accuracy are likely to balk at this, because upkeeping two implements in magical power is painful. Neither the staff nor the orb requires it be the implement you use to make the attack to use its 1/encounter power. Thus, orb or staff wizards may decide to carry a different implement with a high enhancement bonus and spiffy powers to activate in order to take advantage of a different implement type's powers.
Wizards get an amazing advantage in that every time they learn a utility or daily spell they actually learn two (and can prepare one). This means they have access to a good variety of powers for their more infrequent abilities.
It isn't completely clear that when a character gets to swap out a daily power that the wizard gets to swap two - but as swapping does involve selecting a spell that would appear to meet the requirement for being able to do so twice. Presumably you make two swaps in that instance. Some clarification here from the designers would be appreciated.
Rituals also go in a spellbook, and a wizard gains more free than anyone else. These are discussed in detail under rituals below. Control wizards are better at using rituals that require Wis skills. You also get the ritual casting feat for free.
The listed memes (battle and control) have no mechanical effect - we'll consider what's actually good choices for various mage builds. As character creation advice has a history of being suspect in previous editions, I'm going to ignore their recommendations entirely and come to my own conclusions - they may agree sometimes and disagree other times. As it stands, their listed memes correspond well to the two end-member archetypes we'll consider.
Credits and Thanks
For quotes or concept names: Nelyo, Timlagor
And to everyone who's contributed to the discussion - sometimes i've incorporated ideas from it and other times i've disagreed, but its still been interesting.