Player's Handbook[]
Dragonborn 
— The strength bonus is nice for assault swordmages, but intelligence is really the primary goal there. The racial power isn't likely to be needed, since swordmages have few area powers themselves. Their healing surge bonus can be a nice synergy with shielding swordmages.
Dwarf 
— They'll benefit shielding swordmages and those planning on taking Wandering Swordmage, plus their racial feats can add to survivability. Otherwise, though, their low speed and lack of intelligence bonus are going to hurt them.
Eladrin 
— Eladrin are good at either type of swordmage, but assault swordmages can take advantage of the dexterity bonus to pick up heavy blade feats. Teleporting for position may not be necessary for assault swordmages, who can do that whenever a marked target attacks an ally, but the extra skill is always nice. Eladrin Soldier will give +2 damage to all your powers with a longsword at heroic; retrain it for weapon focus (and maybe pick up a superior weapon) in paragon.
Elf — They can qualify for blade feats more easily and elven accuracy is nice, but the lack of a bonus to primary or secondary scores will hurt.
Half-Elf — The constitution will help shielding swordmages and human feats are nice. If your DM lets you use your blade as an implement for non-swordmage powers (a subject that's under debate but may be errata'd), you can grab a nice wizard power or constitution-based warlock power (if you're shielding) with dilettante; otherwise only assault swordmages will benefit much from that ability.
Halfling — Unhelpful stat boosts and a small size limiting the damage of [W] powers makes this a bad choice. Undoing a hit can be nice for a defender, but it's probably not worth it.
Human — Your stat increase will go into intelligence, so you won't get a bonus to your secondary, but the free skill and feat are nice, and an extra at-will is great. The racial feats are nice, too.
Tiefling — These are the most accurate swordmages; they have an intelligence bonus, a bonus to hit bloodied creatures, a power that can give them another bonus to hit against someone that hit them, and a feat to get another bonus to hit with fire powers, or every power with a flaming sword.
Forgotten Realms Player's Guide[]
Drow — Like a halfling, the stat bonuses aren't good, but the racial powers are great, letting you either blind everyone around you (take the feat that boosts the area of the darkness so they either have to attack with a large penalty or move away, giving you an opportunity attack with combat advantage) or have an enemy grant combat advantage to everyone in your party.
Genasi — The stat bonuses are perfect for assault swordmages and the racial powers are all great. Fire punishes someone who hits you, earth knocks prone everyone adjacent so you can have them grant combat advantage, water and wind are good for positioning, and storm boosts lightning and thunder powers.
Dragon Magazine[]
Minotaur (Dragon 369) — They boost both secondary attributes, but only one of those will help and they'll still suffer from the lack of int. Goring charge will only help assault swordmages. Consider khopesh for a heavy blade that qualifies for axe feats.
Gnoll (Dragon 367) — Their stat boosts aren't really compatible; dexterity would help an assault swordmage get blade feats, but the constitution boost is better for shielding swordmages. Pack attack and blood fury are both good damage boosts, though, and ferocious charge might come up sometimes.
Warforged (Dragon 364) — These are better than minotaurs due to their racial survivability boosts. Consider khopesh for a heavy blade that qualifies for axe feats.
Races appearing in the following sources were not intended for use by player characters. Most of these have very limited racial options. Consult with your DM before creating a character using one of these races.
Monster Manual[]
Bugbear — Oversized blades will boost the damage of some powers and bugbear assault mages have easy access to blade feats. Their racial power can give an occasional damage boost, too.
Doppleganger 
— Same stat boosts as a tiefling, but none of the fun to hit bonuses. Still, Change Shape can be fun, and no intelligence boosting race is all that bad for a swordmage. The bonus to charisma and racial Will bonus will help shore up the swordmage's traditional weak defense.
Githyanki — Perfect stats for a shielding swordmage, an initiative bonus, and a racial to fly or make an ally fly (so you can move allies away from dangerous positions with your move) make this a great race.
Githzerai 
— Same modifiers as an elf, without the accuracy power. Their power is nice, but doesn't make up for it.
Gnome — Again with the tiefling bonuses- intelligence is nice, charisma only helps shore up will defense. On the other hand, their racials aren't really great for a defender, who wants to attract attacks rather than avoid notice. Small size limiting the damage of [W] powers and a low speed make this the worst race with an intelligence bonus for swordmages. It's not quite bad enough to be a 3, but you'll want to focus on non-[W] powers if you take this race.
Goblin — Similar stat bonuses to a halfling. Their racial is nice for repositioning in melee and makes it easy to reposition or just walk away from your mark if you want to. They have the same issues with weapons that other small characters do.
Hobgoblin — Shielding swordmages get a boost. The bonus initiative is good and the racial is alright.
Kobold — Like Gnolls, their stat boosts aren't very compatible, plus they have weapon size issues. Shifty is awesome, though.
Orc — Bonuses to both secondaries, but they make better assault swordmages because they can take advantage of the racial healing power- always nice on a defender. Consider khopesh for a heavy blade that qualifies for axe feats.
Minotaur — Oversized weapons push the MM version of this race up. Consider khopesh for a heavy blade that qualifies for axe feats.
Shadar-Kai — Similar to the eladrin, without the benefit of racial weapons and an extra skill. Their teleport is shorter but leaves you insubstantial; it's hard to say that one's better than the other.
Longtooth Shifter —Assault swordmages will appreciate the strength, and the wisdom can be used for Wandering Swordmage. The racial is nice; regeneration (always nice for a defender) and a damage bonus once you've been bloodied.
Razorclaw Shifter — The racial boost to defense and speed once you've been bloodied is nice, the stat boosts not so much.
Manual of the Planes[]
Bladeling — Another dex/wisdom boost, but the racial isn't likely to come up since you have close burst powers of your own.