Kindle (if you like to read)
Movies (keeps track of your DVD's. You can enter each movie just by scanning the bar code.)
Scrabble (You can play against the phone or with others online or with friends)
Words (about the same as Scrabble)
iFitness (for Bowflex users)
Bodybuilding (from bodybuilding.com)
PS Express (Free Photo Shop)
GasBuddy (shows the price of all the nearest gas stations. I use it everytime I have to fill up)
RedLaser (a barcode scanner)
Emojicons (adds emoticons (smileys) to your keyboard in texting and emails)
TWC Max (The Weather Channel)
MyDiary (I use it to keep track of the livestock and any events, breeding, calving, moving pastures, etc)
Office (Same as Microsoft Office or OpenOffice. Has a lot of functionality to its spreadsheets, etc. You can also keep it synchronized with your computer and Google Docs.
mSecure (keeps records of all my usernames and passwords)
Whew.. I didn't realize how many I had and that's not all of them. There is no end to the number of apps and variety as long as your phone doesn't run out of memory.
If anyone you know has an iPhone 4, you can also Facetime with them rather than Skype or any other type webcam. It should already be installed on your iPhone 4. When you bring up a contact in the contacts list, you have options of texting, calling, or FaceTime.
If you open your texting, at the top of each conversation window, you also have the option of calling, texting, FaceTime. If you touch "Contact", it brings up their contact file and you can call, email, etc....
If you have any questions just ask. Did you also notice that with the iPhone 4, you can have more than one app running at a time? If your phone starts to crash on apps, it means you have too many open. Double click the home button and it will show the most recently used icons across the bottom. Touch and hold on one until you see a red minus. Then touch that and it will close each app that is still running.
Good luck. Have fun... you'll enjoy it.
P.S. One other pointer. The way the iPhones are programmed... no matter where you are the phone will always search firstfor an AT&T wifi (if you're with AT&T). If it doesn't find one, it next searches for any other wifi within reach and will display them asking if you want to connect. If it doesn't find a wifi, then it searches for 3G. You could say that is the heirarchy of its design. If you're with Verizon, I don't know how it works. This comes in handy if you don't have unlimited data on your plan. With AT&T anytime you access the internet through wifi, it doesn't come off your data plan.