I know in strategic mode there are no battle animations. But how can I skip them in 3D mode?
Oak's right, there's a setting to turn them off for an entire match. In case you want to do that:
Set Up Game > Advanced Setup > Quick Combat
As pretty as the animations are, they slow the game too much for me so I always play with them off.
Though now that I know Oak's F10 trick (+1, nice tip) maybe I'll consider enabling the prettiness for some matches. :-)
Since version 220.127.116.114, you can enable and disable Quick Combat and Quick Movement in the options menu. Quick Combat will do what you want.
Alternatively, if you want just to skip the occasional animation but let the rest appear, you can just click F10 twice in quick succession. It's a bit silly but it works, especially useful when aircraft are involved.
You can also change the Quick Combat option during the game. You have to use FireTuner to do that (it is a runtime Lua console available in Civilization V SDK). Although doing so is not recommended, I didn't experience any problems so far.
Follow this link if you are interested.