Usually your reel will tell you it can accept sizes up to say 20 lb (for a number to work with) the heavier the line the more difficult it is to handle easily. It won't cast as well, it will tangle more easily, and it will not be as sensitive to the bite.
Keep in mind though, it depends on what your fishing for. I usually stay around 10 lb test line, but when I am fishing for big strippers, or big catfish I change to a heavier line.
You my need to have a bigger reel for this, also a heavier rod.
Especially if you are OCEAN fishing. It can be a little expensive to have all the equipment for all the possible fishing experiances you may encounter.
Back to the question, it is possible to catch a 20 pound fish on 8 pound test line, you have to set your drag, and play them out till they are tired enough to reel in, only problem is if they run and you don't have enough line on the reel to slow them down before they hit the end. I have many rods and reels for different types of fishing, but for fun I love to catch a bass, or any nice fish on an ultra light with 4 pound test. IT'S EXCITING and fun!