Half-Gnome

Everybody knows that Dungeons & Dragons has something of a thing for halfbreed races. After all, the Half-Elf and Half-Orc have been around through almost every edition to actually bear the D&D title. Half-Dragons are one of the more notorious monsters, and the existence of the Tiefling, Aasimar and Genasi obviously supports the existence of Half-Fiends, Half-Celestials and Half-Elementals -- unless you skip the middleman and just make them the half-whatever. Hell, even Half-Dwarves are a thing, by their own name and by the Mul name.

But what about Half-Gnomes? After all, Gnomes are traditionally categorized as being friendly, fun-loving and getting along great with Humans, to say nothing of being open-minded and innovative in contrast to the cautious conservatism of their Dwarven kinsfolk. Plus, they don't have any traditional lore about being a dying race or having fertility issues.
So, you'd think that eventually there'd be a guy with a shortstack fetish that has gotten sick of getting "Ew, you're a creep!" rejections from Dwarf women, and would give asking out the locale Gnome gal a shot; which could possibly result in her saying "Hey, why not, could be fun.", chugging her drink, and enjoying a night together. Really, when you think about it, Half-Gnomes make almost as much sense as Half-Elves do.

Krynnish Half-Tinker Gnomes

However... so far, only one official Half-Gnome race has ever surfaced, in D&D's long array of races. Dragonlance has a 3.5e sourcebook called Races of Ansalon, and in it, we find our first and, to date, only, official Half-Gnome PC write-up. The problem is that Krynnish Gnomes are Tinker Gnomes, hated almost as much as Kender for being portrayed as bumbling idiots, and that lore poisons the results.

See, the whole "thing" for Half-Tinker Gnomes is that they're all legitimately insane, suffering from either obsessive-compulsive disorder or ADHD. We're not kidding here, they do everything but use the names of the illnesses when talking about them. Still, they're not actually that underpowered, even with this trait...

+2 Intelligence, -2 Wisdom

Medium

Speed 30 feet

Broken Mind: A Half-Gnome still suffers under a warped version of the divine curse placed on all Krynnish Tinker Gnomes, afflicting them with either hyper-focus or an inability to properly focus. Choose either the Single-Minded or Jack-Of-All-Trades racial trait to represent which affliction they suffer from.

Single-Minded: Choose one skill at 1st level; the Half-Gnome gains +2 on checks with that skill and always considers it a class skill, but if their skill-points in their "fixation" skill ever fall to equal or lower than their level, they suffer a -2 penalty to all other skill checks until they raise it higher again.

Jack-Of-All-Trades: The normal set of class skills no longer applies to this Half-Gnome. Instead, they treat all skills as class skills, but they cap all skills as if they were cross-class skills. However, they gain synergy bonuses at 3 ranks per skill rather than the usual 5 ranks per skill.

+2 racial bonus on will saving throws.

Favored Class: None. A multiclassed Krynnish Half-Gnome must keep its classes balanced with each other or suffer a -10% experience point penalty.

Tellenish Half-Gnome

Whilst the Krynnish Half-Gnome is the only official Half-Gnome in D&D so far, there is an alternative. Kingdoms of Kalamar introduced its own, far less annoying take on the half-gnome in Dangerous Denizens: The Monsters of Tellene. Tellenish half-gnomes are sometimes born of arranged marriages, just like the Tellenish Half-Dwarf, but less frequently. More commonly, the result from one-night stands that have a long-lasting after-affect; usually, these are the result of Human females being wooed by pervy Gnome males, but obviously you could always play the other way around - why should Human guys turn down the shortstacks?

Tellenish Half-Gnomes are often mistaken for unusually short humans; standing between 4' and 4'6" tall, their only real difference from ordinary humans is the slightly larger than average size of their ears, eyes and noses.

Naturally adaptable and light-hearted, half-gnomes get on well with almost everyone, even hobgoblins and their halfbreeds, although orcs are a rare exception.

+2 Wisdom, -2 Strength

Medium

Base land speed 25 feet (15 feet in Medium or Heavy armor)

Low-Light Vision

Gnome Blood: A half-gnome is treated as a full-blooded gnome for all special effects that key off of race.

+1 racial bonus on saving throws vs. Illusions.

+1 racial bonus on Craft (Alchemy) checks.

Gnomish Lineage:

A half-rock gnome (daruukala) has a +1 racial bonus to Listen checks and a Favored Class of Bard.

A half-forest gnome (shinamar) has a +1 racial bonus to Diplomacy and a Favored Class of Rogue.

A half-deep gnome (shimyth) has a +1 racial bonus to Fortitude saves against Poison and a Favored Class of Fighter.