I have two favourite races - one Alliance and one Horde. Like I mentioned above I have loved these two races from day 1. Infact, they we're the first two races I rolled of each faction, respectively. If you could only ever play two races I'd play these. SpaceBard mentions a massive server crash in his answer and yeah, these races would be the two I'd pick from when starting over. Further, if my chosen Horde race was playable as Alliance too I'd [probably] never visit the dark side (and vice-versa)!
So, without further ado my two races are: Gnomes and Taurens!
I currently have two Gnomes on my home Alliance server. One is a mage, the other a DK. They are my second and third character's respectively. I've always loved the Gnomes and my first character was my Gnome mage. I love how they look, their funky hair styles (in particluar the beehive), thier bright hair colours. I don't really pay much attention to their moves in game but I know my mage chucks her arms in the air when casting Blizzard which looks pretty funny and my DK has some pretty amusing melee moves.
On a slight tangent, two other races that I really like are the Draenei and the Goblins. Again, I love the ability you have as a player to customise how they look - with Draenei horn styles and Goblin ears & noses. My main is a Draenei and I have a really low level Draenei which I'm attempting to do the Ironman Challenge on (I should really get back into that). I don't have a Goblin currently despite having completed the starting area 4 or 5 times but in the future I intend to have a Goblin rogue on my Horde server.