What races have Spider Climb as a racial trait according to official WotC materials? I know Chitine have it, but who else?
Looking it up, I find that the Katane template (half-vampire, Dragon Magazine #313, p64), also gets spider climb.
These races have Limited versions of spider climb: Immoth (Monster Manual II, p128) and white dragons get Icewalking (spider climb on ice and snow), and copper dragons and sapphire dragons (Monster Manual II, p84) get spider climb on stone.
Each of these are Extraordinary abilities, except the hooded pupil's, which is Supernatural.
Since the chitine can climb 'as if under the effect of a spider climb spell', and has a listed climb speed, these races, which gain a climb speed instead, may bear consideration as well (although spider climb is better than a mere climb speed, due to not requiring climb checks):
The forestkith (Monster Manual III, p64) jungle and snow (Frostburn, p136) goblins have a 20' climb speed (jungle goblin is LA +0 and it can use Dexterity rather than strength for climb checks). The grippli (Dragon Magazine #324, p87) has a 20' climb speed as well. The arachnoid and chameleon creature templates (Underdark, p80, 83) gain a climb speed, as does the Nimble Skeleton template (Libris Mortis, p162). The nether hound template (Dragon Magazine #322, p89) also gains a climb speed.