Well, slim glass filter or wide-angle slim filter is for use with - you already guessed - wide-angle lenses. If you are using a full frame camera such as a Canon 5D or 1Ds, you'll probalby need one of these from 24mm (or even 26mm) and wider lenses. The drawback is that slim filters don't have front threads and therefore you cannot attach conventional lens caps.
See photo below to see the difference...
You also may want to read this discussion as well as this one.
I usually don't use filters for protection except when weather/conditions are really bad (sand, sea spray etc.). Try to stay with a good brand (B&W and others mentionned above) but I have a friend who claims that Hoya HMC () is OK.
When I first started out in photography with my Nikon F, all the common lenses were 52 mm diameter and I needed only one set of filters for all my lenses, but now with zoom lenses and many telephotos, one has to have other diameters such as 67 and 77 mm. To some extent one can use adapters to reduce the thread size of the filter, but the reverse may cause vignetting.
Also, the thin filters are necessary with some wide angle lenses to avoid vignetting, and this may apple to some wide to tele zooms. These thin filters are more expensive. I have a a regular 67 mm B + W filter for my 18-70 mm Nikkor DX and it seems to work OK (the lens has vignetting wide open anyway).
It really looks strange to have a 77 mm filter on a 52 mm filter diameter lens, but it does work.