Usually when your computer is running short on memory one of two things will happen. The computer will crash or it will "swap" things out of memory onto the hard disk to be saved for later. Hard drives are not nearly as fast as regular memory so this slows things down drastically if it starts to happen a lot. This is probably worse on laptops as they usually have slower harddrives.
A quick easy test would be to notice if your hard drive seems to be running flat out when you notice the computer running slow. You can also open task manager (press ctrl-alt-del and select "Start Task Manager") and switch to the "Performance" tab. Depending on the OS (assuming windows) you should notice a box that says "Physical Memory" and one of the fields should be "Available". If this available memory is very low you could be having problems.