Current iOS devices running iOS 5 (iPod Touch, iPhone, iPad) are capable of being standalone devices. You do not need a computer to use them.
The term "iTunes" can refer to two things...
The iTunes application, which you seem to take issue with, and the iTunes store, where you buy apps, music, movies, etc..
You do not need iTunes (the application), but you will find it difficult to avoid using iTunes (the store).
iTunes (the application), makes it possible to use iTunes (the store) on your computer. This can provide some convenience, but is not necessary.
As long as an iOS device can connect to the Internet, you can activate it without a computer or iTunes (the application).
iCloud provides several features. None of them really replace iTunes (application or store).
- iTunes in the Cloud: You can let Apple store the music you've purchased from iTunes (the store) on their servers and download them on demand (actually, they just store references to which songs you own, they already have all the files stored for iTunes (the store)). If you sign up for iTunes Match, they'll also store references to your music that is in your iTunes (application) library but wasn't purchased from Apple. They'll also upload and store your music that they do not have in the iTunes store (within limits).
- Photo Stream: Syncs your photos across all of your devices. Additional features apply to users of iPhoto or Aperture.
- Documents in the Cloud: store your docs on Apple's servers, access & sync them between devices (requires apps that have been written to take advantage of this feature).
- Backups: Back up your device's data to the cloud
- Sync Apps & Books: Apps and Books purchased through iTunes (store) and the iBookstore (an extension of the iTunes store) can be synced to multiple devices.
- Sync calendar, mail, and contact data. Comes with an @me.com email account.
- Find my Friends and Find my iPhone: lets you GPS-stalk your friends and family and track your phone if you lose it. Find my Friends can be useful at big gatherings, and it can be toggled on and off at will in case you don't want your mom to know you're hanging out in the seedy part of town.
I hope this is helpful.