Yes, use a divider - a thick cardboard covered in foil or plastic wrap that fits tight from side to side OR you can just pour the one batter in the pan; set it slightly propped while making the other batter & add that. The two will join somewhat in the center and bake as one cake. You won't have a perfect join but who cares? 
A few servings will have a bit of both flavors - sort of like a marble cake.
Years ago I made a cake for my brother who only ate vanilla while the rest of us only liked chocolate. I was using cake mixes back then, they were pretty thick batters so I poured one flavor into the pan first and tilted the pan to one side so it would stay there and then poured the other flavor into the pan and swirled the middle to make a slight line of marble cake. it baked up just fine and stayed separated. The only trouble I had was that one flavor baked higher than the other so my cake was severely lopsided. I was a teenager then so I didn't know anything about leveling a cake or anything so it was a little messy but worked out just fine. I think now, I would probably recommend baking them separately just icing them side by side.
http://www.cakecentral.com/cake-decorating-ftopict-605736.html
Heres another thread all about it !
They won't mix .... It's thick like lava; it's not watery like Kool-Aid. When the batters meet in the middle, they stop each other. I just prop one end of the pan up and pour the batter in one at a time. I never use a divider. Customers dont' care if they are not exactly half .... they actually like the middle part where it's mixed.
dupl thread ... see other responses at http://forum.cakecentral.com/cake-decorating-ftopicp-6189933.html#6189933
I just done my first one of these about a month ago. VERY EASY...I just rolled a hand towel and propped it up on one end and poured batter #1. Then as I was pouring the batter # 2, I gradually laid the pan down flat. It worked perfectly...
I use to make 2 cakes to get 1/2 and 1/2, NEVER AGAIN....
I did it with a 1/2 sheet. Make sure your recipes are somewhat the same. I had a chocolate cake that was too dense and didn't raise enough to match the Vanilla side, so I ended up cutting the Vanilla side off to level. Also, it really helps if you make up one batter, then the other batter, and pour them in one right after the other.
Also, don't forget to prepare your pan ahead of time. 
(not that I ever do that...heh heh). Sometimes you get so caught up in getting the batters done, the pan gets forgotten about. 
I made a lemon and chocolate 1/2 and 1/2 just last week. I did use a quickie cardboard divider (just while pouring the batter) because I didn't want the batter to run too far up the side if I tipped the pan too far. I'm much better with my pans flat!! At any rate, I've never had a problem before, but apparently these batters were too different... the chocolate baked quite a bit over into the lemon side. It raised much higher and it seemed to have a life of its own as it covered almost 3/4 of the pan!! I think it had to do with the lemon batter... it was much thinner than the chocolate. All that being said... I still used the cake and the customer was still more than happy! Good luck.
j-pal, that's common with chocolate ... chocolate cake rises higher and spreads further than other flavors. That's why when I do a 12x18 that is half-n-half, I use one part chocolate and 2 parts white cake ... it ends up being about 1/2-n-1/2 bcause of how the choc bakes.
indydebi, thanks. I've done 1/2 and 1/2 with chocolate and multiple other flavors before and while I've had experience with the chocolate raising higher and better, I'd never done it with the lemon before. I was just surprised at how LITTLE the lemon rose! It's a good tip about using less chocolate batter than the others, though - thanks.
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