It is possible to run a 4E combat without the use of hit points for either the characters or monsters, by utilizing the 4E skill challenge system. This will alter the game. You will simplify the combat but also allow the DM to be more cinematic in the storytelling. You will undoubtedly come across situations that will require you to make use of house rules.
The first thing you will have to decide is the use of at-will powers. Characters have more than one at-will power and since each power has an unlimited capacity in the number of times it can be used, players will min-max one at-will power and disregard the rest. Further, players will eventually drift toward the Essential character builds because those builds already simplify the combat and begin the min-max approach to the at-will powers. None of this should necessarily be a concern if the DM is already considering using this skills challenge approach in order to emphasize the cinematic storytelling over the tactical maneuvering in combat.
If for some reason, you as DM do not want the characters to focus on just one of their at-will powers you will have to devise a house rule. For example, all at-will powers of the same type (melee or range) a player must utilize before that player can utilize again any at-will power of that same type, which the player has already utilized more than any other at-will power of that same type. Players, however, will simply minimize the number of at-will powers of a single type altogether. Fred (first level) only has a basic melee at-will power, which is at +10. The players are simply following the course already set: simple combat in exchange for cinematic storytelling.
As a side note: one can look at the current 4E combat system as an attempt to create a formulaic approach to cinematic storytelling in the tactics of the characters. The formula spells out the cinematography in the individual power descriptions, although much more limited, and can be at times ignored by both the players and the DM, depending upon their preference. The skills challenge approach puts the burden of cinematography back on the shoulders of the DM, which will not be to everyone’s liking. However, a DM who likes to tell stories and players not comfortable describing their character’s actions might find the skill challenge approach more to their liking.
Assuming the players simplify their character builds and drift toward the Essentials, the problem of magic missile will become apparent. It is an automatic success and an at-will power, a veritable machine-gun in a sword fight. The higher percentage of the party members who can cast magic missile makes the party that much more unstoppable. A party of one who happens to be a magic-missile throwing character will automatically defeat every skill challenge.
In order to avoid that scenario we suggest the DM limit magic missile and any other like power to counting as a success but only in regards of having the advantage characteristic of removing a failure, counting as one of the available advantages in the skill challenge. Magic missile does not count as a success for the overall number of required successes: a player can only utilize magic missile if the skill challenge grants at least one advantage: and, magic missile takes up one of the slots available for advantages. Magic missile still retains its usefulness but does not overpower the skills challenge approach.
Establishing the target DC is simple and does not deviate from how a DM establishes the target DC of a normal skill challenge (as written in the Rules Compendium).
Example: You have four first-level characters in the party. Turn to page 285 and multiply the number of characters by the number cross-referenced by their level in the column “XP per character”. That number is 100. 100 x 4 = 400. "400" is the XP limit on a standard encounter for four first-level characters. Turn to page 294. Starting from the top left corner in row 1 of the “Level” column go across and then down until you reach the first appearance of 400. “400” appears in the first row under the column “Complexity 4”. The first row tells you the level of the skill challenge and the column where you found the number tells you the complexity of the skill challenge (Level 1: Complexity 4). Turn to page 159. Find the complexity on the table to determine the total number of successes required, the breakdown of successes between moderate and hard, and the number of slots available for advantages (10 successes, 4 advantages, 7 moderate and 3 hard). Turn to page 126. Find the level of the skill challenge and determine the target DC for both the moderate success and hard success (moderate DC 12, hard DC 19). You now have all the necessary information to run a standard encounter combat. The party needs ten successes before three failures. The party needs seven successes at DC 12 and three successes at DC 19. The party has slots for four advantages. You can find a list of sample advantages on page 160. (Make what you will of the advantage talking about an easy success: we have no opinion on it.)
For easier encounters follow the same procedure but assume the characters are one or two levels lower. For harder encounters follow the same procedure but assume the characters are two to four levels higher. Personally, we suggest one level lower for easier encounters and two levels higher for harder encounters.
We had the character builder create a half-orc slayer at 30th level to compare the bonus to hit to the moderate and hard DC target numbers at thirtieth level. The character had a +38 to hit against a moderate DC 32 and hard DC 42. An elf illusionist at thirtieth level had a +27 to hit. It seems plausible that the skills challenge approach will work through all the levels. Considering your personal preference and that of your players, you might want to put an automatic level adjustment (up or down) on the characters for the purposes of encounter designs. Presumably, your adventures are not all combat and skill challenges actually requiring the use of skills will be necessary. Otherwise, expect a party of slayers who know nothing outside of swinging the sword.
Both the slayer and illusionist had +6 items boosting their attacks that would otherwise be +32 for the slayer and +21 for the illusionist. If every character in the party is +32, then you might want to do a level adjustment upwards. If every character in the party is +21, then you might want to do a level adjustment downwards. (Note: A single level adjustment will not alter, up or down, the target DC by more than a point. Our preference is to have a difference of eight between the attack bonus and the target DC. A target DC 32 needs an average attack bonus between the party members of +24. The slayer and illusionist with their items have an average of +32 eight points higher than 24. We would simply adjust the respective moderate and hard DC target numbers by those eight points to a DC 40 moderate and DC 50 hard. Problem solved for our preference.)
Without hit points, how do you determine if a character dies? We suggest whenever a player rolls a “1” on a d20 the player immediately rolls again. If the second roll is not at least a moderate success, then the character is unconscious for the encounter but another player can bring back the unconscious character through healing. If the character is unconscious, then the controlling player immediately makes a third roll and if the third roll fails to make an easy success the character is unconscious and dying. The character cannot be healed until the character has failed at least two death saving throws or has stabilized by succeeding at a death saving throw. Lastly, it is always the discretion of the DM to coup de grace an unconscious character.
The benefit of the skills challenge approach is that you are free to use your imagination and there is nothing for the DM to track other than what the players roll and the description of the encounter. Monsters do not roll to hit. Monsters do not do damage. Monsters can do whatever they wish. Pick up a character and throw the character across the room into the wall. Let the monsters break the characters’ bones, gash their flesh, burn and mutilate them. There is nothing preventing you from describing a combat with hordes of undead and/or with an ancient red dragon against your first level characters. Describe as many grizzly deaths and kills as you like because you can just keep pouring in more monsters until the party succeeds at the combat skill challenge. The characters can take the abuse no matter how badly you describe it.
One final thought, since the number of total required successes is never more than 12 and you can never have more than three failures, the more characters in the party the quicker the combat will be over, either through accumulated successes or failures. The party size does increase the target DC for successes. A party of twelve characters might not even allow every person to participate in the combat. If this problem occurs, then you might have to resort to a house rule such as increasing the number of total required successes and/or increase the limit of acceptable failures.