I left cake batter out for about 2 hours at room temperature. It's got three eggs in it. Is it still good or should I start again?

I'd use the family vs. customer rule here--fine for family, not fine for customer. The reason isn't health related--with all the sugar in it, it should be fine.

The problem is that the leavening ingredients have been working for 2hrs. already, so that will probably result in an odd texture, and perhaps oddly shaped, cake. You may wind up with a very light, crumbly cake with a high dome, or you may get a very flat cake that sinks in the middle--depends on what's "gone" from the mixture having escaped while sitting out. It may look fine after baking, but the texture will be probably be off.

If any of the above issues is a concern, I'd re-bake.

HTH
Rae