oh god so many!!!!! nb all of these i mention are iphone/ipad - they may have droid equivalents but i'm not sure...
i think my all time favourite is more toast! by maverick, which lets you make virtual toast (or toaster pastries, crumpets, waffles etc) and put virtual toppings on them and virtually eat them. they have a whole range of apps along the same lines: sundaes, cupcakes, cookies, grill, salad, pizza are the ones i can think of. they're $0.99 i think. they're more amusing than they sound, you can share photos of your toast/cupcakes etc on FB and so on
i really like a lot of card games, solitaire city is great for time killing, it has tons of variations on solitaire. not cheap but worth it. i use it every day at least once.
pocket god is pretty silly but a lot of fun for just pootling about, you get a little island and you can create people and then make them do stuff like build houses or ride dinosaurs and so on, or just kill them in a variety of fun and twisted ways
the new tetris app is truly fabulous on ipad, maybe somewhat less so on iphone.
for anyone into baseball (especially if you live outside the us and so don't have all the usual coverage on tv/radio) the MLB at bat app is brilliant - it's not cheap (about 15 bucks i think) but it has everything - live box scores, live text commentary, live internet radio feeds (you can choose whether you listen to the home or away team), video highlight clips etc - you can pick favourite teams so they list first or look at the whole division at once. it's good on iphone but on ipad it's stunning! on iphone when bases are covered they just have a little square dot, but on ipad it puts a picture of the runner on the base, it's just little differences like that but it makes a huge difference to the feel of it. also the ipad version has a little mlb newspaper in it so you can read the latest stories etc. it's really really good.
there are loads of others i really like too - i'm a bit of a fiend for "useful" ones, i love weather apps (because weather kinda fascinates me), but also apps that do things like calculation, taking notes, currency/unit conversion, they're really useful to have.
oddly the ones that aren't so good tend to be the social networking ones - twitter for iphone/ipad is ok but not spectacular, same for facebook. lots of the others like yahoo and so on are just plain old crap. the only one i really rely on is hootsuite, which is, imho, the best twitter client around.