Any iPod and iPhone apps that you can recommend?

Theres a new one thats pretty cool called "Talking Tom Cat".

As far as I know, any and every app (besides things like iMovie) are compatible with any iPhone.

Pocket God is a pretty fun game if you want to waste time.
Angry Birds is a good game where you shoot a bird at a building and you have to make it fall down.
iShoot is a very fun tank game.
Flight Control is a very fun game where you have to land the planes on the right airstrip.
iBooks is a very good free application if you like to read.
Cooking Mama is a good game if you want to cook virtual meals.
Skype is good for chatting with people (not sure if it supports front facing camera on the iPhone 4, but I'm sure that it does).
Pandora is good for listening to music. Now with iOS 4, you can listen to Pandora while you play other apps.
Kindle is another good (free) application if you like to read, and you don't want to use iBooks, or iBooks doesn't have the book that you want in it.

Well, I think I've listed enough. I know that I forgot a lot of apps, but if I remembered them all, there would be a list too long to read in one day. I think that this should get you going.