I'm taking classes at a Community college, starting my 3rd semester. I've taken stick / oxy-fuel, MIG and will start TIG in a few weeks. The prices here are quite reasonable, I think I've paid $46/unit and they are 3 or 4 unit classes so less than $200 per semester.
Cost varies by state, I've come to realize California community colleges are relatively cheap, some states you would pay $1000+ for these classes.
The biggest thing the classes have provided for me is organization (what welds to do, in what order), enforced practice time and fairly immediate feedback.
If you are disciplined enough to put in several hours a week practicing bead after bead, and use a good text and some youtube videos (I like Jody at Welding Tips and Tricks), there is really nothing stopping you from learning on your own.
The main advantage I got from class was 6 hours a week welding, and an instructor who could look at my welds and verify I was doing it right or identify what I was doing wrong and offer some correction.
Having a good welder help you is great, but just being able to lay down a good bead, doesn't mean they have the teaching ability to help you do a good weld. It is nice having that person who can actually tell you what you are doing wrong, not just tell you your weld looks like ****.