The three graphic software products I'm most familiar with all come with some nice built-in filter effects. Photoshop seems to have the most, which is probably one reason it's become the industry standard. I've found that there are ways to reproduce most--if not all--commonly used filter effects in Paint Shop Pro. Sometimes PSP has similar built-in effects, and sometimes it requires a work-around. A lot of filter effects can be done manually, but the filter makes them quicker. In addition to built-in filters, there are user-made plugins, and collecting them can get a little overwhelming after a while. It's hard to remember which ones do what, and there are many similar ones out there.
My go-to filter set is a freeware collection (Visman or "VM") that I've been using since I first got Paint Shop Pro. I found it on a tutorial site that no longer exists. There are several sets and a total of around 70 filters in all. In PSP, they appear in your Effects menu and each set has a submenu titled VM (something.)
These are primarily distortion filters. If you're looking for artistic, painting effects, etc I recommend Xero Filters.
As for the VM filters, some are more useful than others depending on what you do. For the most part, I make 2D collages and photomanips, or I make graphic resources. So the ones that are useful to me may not be useful for someone else. Some produce similar effects while others are really unique. So what I want to do is provide an example gallery for each set. There used to be some good ones online, but I haven't been able to find one, so I decided to make one myself. It's going to take me a while to get them up, so check back if you're interested.
These example galleries do not contain finished artwork. All I did was choose a free, public domain image and run the filters on them to show what the effects look like. When I use the filters for finished work, I will link to it from here.
VM Instant Art