If you have a bunch of programs running at the same time (especially if they're memory intensive, such as graphics software) you'll almost certainly notice an improvement.

If you don't have a lot of RAM, the programs start using the hard drive as a "scratch disk," dumping and retrieving things as required. It really slows down the show. Add more RAM and you can push things much farther before the HD is used as virtual RAM again.

If you have some really big files, such as PDFs, Powerpoints, etc, open up a few of them simultaneously and see how your system handles the load. Can you jump from one to the other fairly quickly? Try opening several instances of your web browser at the same time.

Other considerations include operating system (Microsoft Vista uses far, far more memory than something like Linux, for instance, meaning Vista should get more of a kick in the pants from an increase in RAM) and your video arrangement (dedicated card vs a segment of RAM, for example).