Client-side validation just avoids the client from going “but I filled this all in and it didn’t tell me anything!”. It’s not actually mandatory, and in reality, client-side validation is a very new thing (read: 5 years old or less). In practice, all it does is prevent your client (with JS enabled) to know whether the form is okay before reloading a page.
If AJAX is in the game, it is different – it allows you to save bandwidth as well as to provide user with feedback before submission.
Finally, if you’re building strictly client-side, peer-to-peer exchange apps (think games), you’ll want client-side validation to keep the clients from cheating.
Server-side validation is also crucial due to the fact that client-side validation can be completely bypassed by turning off JavaScript. In a way, JS-driven validation is a convenience and an aesthetic/cosmetic improvement and should not be relied upon. Furthermore, it is trivial to edit the source of a page locally in order to disable or bypass even the most complex of JS validation.
What could a user do if you do not server-side validate? Anything, depending on how you use their data. You could be allowing users to drop entire databases (or worse, leak them), modify anything they like (or worse, read anything they like. Directory traversal flaws are extremely common entrance points for naughty people), and elevate their privileges at will. Do you want to run this risk? Not validating user input is like trusting people and not installing locks on your house.