If Bitcoin became widely adopted, it could (and probably would) function exactly like any currently popular fiat currency. (Dollars Euros Pounds Etc.)

There's no real functional difference except that there wouldn't be a government that could print more money, therefore I see no logical reason that credit and banking would not work the exact same way it does currently.

With banks currently, if, say, $1000 was deposited with a fractional reserve of %10, the bank would then loan out $900 of that same $1000 to other people.

All you have to do with is replace the above $ with BTC and you have the exact same system using Bitcoins. There's no reason this couldn't work with banks, credit card companies, loan agencies etc.

Now if you were to question whether it's likely to happen currently, that's another question, but once the price stabilizes and adoption becomes high, I guarantee you'll see Bitcoin banks and credit agencies.