It's going to depend on what you want to sync and what you want to sync it with. There is no one-size-fits-all solution.
Quite a bit can be synced between iOS devices using iCloud. New purchases from iBooks, iTunes, and the App Store can be automatically downloaded on all other iOS devices using the same Apple ID. Purchases from Apple's iStores are also available for download to any of your compatible iOS device that use the same Apple ID.
Mail, Notes, Contacts, Calendars, and much more can be synced between different iOS devices using the same iCloud account.
Mail, Contacts and Calendars can be synced across most other devices if you pick the right service; Google/GMail being the easiest.
And some things simply require a computer, if not running iTunes then a third party program. But there are workarounds for most of those things.