It depends on what kind of programs you're running and how many of them you are running. For me, I like to keep open Agent, Internet Explorer (several windows), Windows Explorer, Eudora, possibly ACDSee, and maybe a few others. Since I also run antivirus sometimes, Norton Protected Recycle Bin, and the ATI multimedia center, 128MB doesn't go very far if I happen to run something memory intensive. I was seeing a large dip in resources on occasion and some disk thrashing as my main memory was used up. I don't see that anymore with 256MB.
If you use graphics programs, then you'll see the benefit in working with large images, such as those commonly created by a scanner (mine can create some monsters when I go for maximum detail -- try loading a 40MB image with a small amount of RAM).
For most people, though, the extra RAM is worthless. I could afford it, and it makes my computer a little more able to handle any heavy tasks I throw at it. As you said, it doesn't show any improvement in games, however (at least that I can tell).