I have a 2002 Volkswagen Golf with a 2.0 engine. The 'check engine' light starts to blink and the car starts to shake violently, and it doesn't accelerate past about 25km/h. Then after riding it that way for a few minutes, the engline light stops blinking, and just stays on. The car shakes a little bit (not as violent), and the car accelerates past 25km/h but has a hard time doing so. I've taken it to the mechanic and the first time, they replaced the catalytic convereter and the spark plugs. The second time, they replaced my O2 sensor. None of those things seemed to help.

There are a LOT of problems that could have this effect on an engine ... but from this description it sounds like your timing chain might have skipped a tooth. If your timing is off, the pistons will not fire at the correct time, and will cause a violent shake in the engine, and the engine will lose almost all power. This issue would also cause a hard start whenever you try to get your car started, so it may not be this ...
You might have a leak in your head gasket which is leaking either water or antifreeze into one of your pistons. When you start the car, is there a sweet smell in the exhaust? If antifreeze gets into a piston, it usually stops that piston from firing at all. This could cause a violent shake in the engine, and might not cause a hard start, so it would only be noticed when you start driving.
You could have a dead spot in your distributor cap -- the piece of the engine that distributes electrical charge to the spark plugs. Replacing the plugs is a first step to finding out if it is this problem -- it is cheaper and easier to do than replacing / repairing the distributor cap. When the plugs don't want to fire correctly, it has the same effect on the engine as antifreeze in your engine -- a violent shake and diminished power.
There is a SMALL possibility that it could be your transmission. If your transmission is getting stuck in the wrong gear, or between gears, the engine will try to pour out power, but will get so bogged down by the malfunctioning transmission that the whole car will shake. This is a VERY rare problem, but it does occasionally happen.
Your car's computer might not be sending or receiving the correct information to or from the engine. If this is the case, it could be pumping a different amount of fuel to each cylinder, causing the engine to fire too hard sometimes, and too soft other times. This would prevent you from getting proper acceleration, and could cause a shake in the car, but I don't think it would be a Violent shake like you described.
You could have a bent Cam, which would not allow the valves to function correctly (but this would probably keep the car from starting). It could be a bad bearing in the engine (but this would probably keep the car from starting at all). You could have faulty valves (but once again, it would probably not start at all). There are a lot of other possibilities as well ... but I think you get the point here. It is going to take a while to figure out exactly what is wrong. If you have a friend who is willing to help you out, or a really cheap mechanic that you can take it to, you'll probably save a lot of money over taking it to a corporate shop. Best of luck!