In Search of the Best Egg-free Cake

I turned vegetarian in May. I don't miss the meat but I do miss eggs and what i could turn them into in the oven combined with flour and butter and sugar. I used to believe and still do that an egg-free cake will never have the same depth of flavours and texture that one with eggs has. I'm just hoping that vegans the world over have found a way. And with that, I'm out on a search for a great egg free cake that I can bake and eat with a feeling of satisfaction. I'm not looking for 50 different types of cakes. I just want a handful of my favourite tea-cakes - vanilla butter, dense chocolate, carrot, banana, lemon drizzle.

On a side note, if this doesn't work out, I can always fall back on breads and pies and cheesecakes which always taste better to me without eggs to begin with.