Can I use an iPad effectively without a computer to dock it to?
If you get a 3G iPad, I think the 3G data plan has to be activated through iTunes.  If you get Wi-Fi-only iPad, this isn't an issue.

Note that you can probably get by if you have a friend with a Mac or PC who will let you sync once in a while for these rare needs.

Syncing is also useful for these needs:


Backup
Transferring photos (although you can e-mail them instead)
Syncing calendar and contacts
Getting music, videos, and books from iTunes Music Store (you can d/l songs over the air, but I think the other media types have to be done through desktop)


But if you don't need those areas of functionality (and many people won't), then you won't miss syncing.  Basically, if you don't expect to use Apple's built-in apps, you won't need sync.

MobileMe is really only useful if you have a Mac or PC.  It makes it easy to sync calendar and contacts across multiple machines over the air.  A few third-party apps use it as well, but not many.

Third-party apps typically sync over the air, because Apple's sync is not very open to third-party developers.

FWIW, since getting my iPad, the only time I turn on my MacBook is when I want to backup/sync purchases or charge my iPad.  I'm not saying that the iPad is a complete substitute for a laptop, but it is definitely a useful device all by itself.