If there's one race with an identity crisis it is those vague kind of dwarves, kind of halflings, ugly short statured gnomes. They conjure an image of blue and white striped vests, pointy red hats and white beards, one foot guardians of your grandma's patch of chrysanthemums. In mythology they tend to be no bigger than a squirrel, living within the trunks of trees. They give presents to good little Scandavian children with their tiny magic goats. In the Land of Oz they are mischevious antagonists with many characteristics akin to goblins (indeed, gnome and goblin meant the same thing in Romanticism literature). In more modern iterations they are garden ruining groundhogs (Harry Potter) to technological savvy tinkerers (World of Warcraft). Pinpointing the gnome culture can be...a challenge.
A lot of DMs like to go the tinkerer route. Others like keeping gnomes forest dwelling fey living in small villages, somewhat primitive. Still, others like to not give their gnomes any real flavor at all, many times omitting them from their world completely, which is sometimes the easiest solution to the gnome question. Gnomes in my world tend to be business savvy entrepreneurs, friendly (for the most part), cunning wizards and bards that tend to avoid adventure for more realistic goals, but I have to admit...they aren't exactly as iconic and fleshed out as elves or dwarves. We all have a certain stereotype when approaching the D&D races which come from classic high fantasy literature (Tolkien being among the most influential). Elves are mystical, magical, wise and elegant. Dwarves are loud, raucous, honorable and stubborn. Halflings almost universally adhere to hobbits (though a little more outgoing). Where gnomes fit in this classic fantasy realm is often times up in the air. Gnomes can sometimes be evil critters that eat children in the night. Terry Brooks' gnomes from the Shannara series are yellow-skinned and tribal like, though Brooks inserted a few different sub types of gnomes, it's not clear what place they fill in the greater fantasy realms. Dungeons and Dragons perhaps has done the most for gnomes, fleshing out their history and culture in several different campaign settings but even still...it feels lackluster. They weren't even in the 1st Player's Handbook in 4th Edition in favor of Dragonborn, Teiflings and Eladrin (some would say much "cooler" races to play) but for me...I've always had a soft spot for gnomes.
Perhaps it's the gnomes' refusal to be type-cast into one thing or another that is appealing. Yes, there are some characteristics that are standard across most literature: gnomes are tricksters, sometimes using magic to fool people, and can be a simple prankster to a homicidal illusionist. There's certainly a niche that they can fulfill, but when we think of rich interesting cultures in fantasy lands gnome is hardly at the tip of our tongue. Comic relief is more like it. So, when people say, "Let's get rid of the gnome," I can't really blame them, even though I really like those little runts. Playing a gnome can be like playing with a clean slate, whereas your elf, dwarf or halfling have to go out of their way to not play into stereotypes, gnomes can be whatever because they've never been so intricately explored.
This is, of course, adhering to "classic" fantasy definitions. Elves, dwarves and halflings can be whatever you want them to be within your world. It's fun to see the ever popular table of drunken dwarves throwing insults at the elven scholar at the bar while a halfling barmaid quips jokes trying to juggle a tray of frothy steins, it's a classic scene and makes for a good time and we can all picture it easily...and the gnome...well, he's sort of in the corner maybe...doing gnome stuff. I like roleplaying in "classic" high adventure, high magic, high fantasy settings - it's what got me interested in D&D all those many years ago and I've kept with it and when I started DMing I took a look at the gnome and mulled that mysterious race over in my mind a bit.
In my world gnomes became scholars, not necessarily wizards, but traditional scholars of history and science. They are skilled astronomers and cartographers; if you want a map consult a human but if you want a work of art, consult a gnome. They adore magical trinkets and items and study their properties with the utmost care. They are in the business of making magic a practical application of everyone's life: an unseen servant in every house and ever burning candles at every dinner table. They prefer the city, blending in nicely amongst the other races, opening up shop (and the most successful shops are usually owned by financially gifted gnomes), they make the most out of opprotunities, are generally accepting of everyone, are skilled advisers, fortune tellers, storytellers and distillers of fine liqueurs. Long ago they abandoned their life amongst the fairy-folk out of curiousity and never looked back. My version of the gnome, however, is not the same version everyone else has (although mine borrows heavily from the "norm" of gnomish behavior) but that's the beauty with the gnome - there's some flexibility there.
Okay, yes, I know, there's flexibility everywhere. It's Dungeons and Dragons. Make your elves blood thirsty cannibals and your dwarves jungle dwelling mystics. That's fine. I mean...some people may have a problem with it but who cares, your table, your world, your rules. But in turning elves into bloodthirsty cannibals and dwarves into vine swinging Tarzans feels unnecessarily forced to some people...whereas the gnome...he fits right in there (for the most part) and I think that's great!