Would I hire a designer or programmer who doesn't have a college degree and learned everything himself on teh Interwebz?
Fuck yeah, I do it all the time.
Ok, now let's assume I'm involved in a car accident and need surgery.
Would I want that surgery to be performed by someone without a degree and who learned everything himself on teh Interwebz?
Fuck no!
So to answer the OP's question, it depends on the degree.
In some cases (when it comes to things like design/programming), obtaining a degree is pretty much pointless because learning everything yourself isn't all that complicated logistically speaking. If you have a computer and an Internet connection, you're good to go.
In other cases though, when it comes to doctors/pilots/whatever, things are a bit more complicated because you need access to very expensive devices, because it's much more important to learn from professionals (as a designer or programmer, you don't need to be in direct contact with the person you're learning from but as a surgeon... you get the point) and so on.