I'm pretty black & white on the issue of mounting stamps. I absolutely think that you get a better stamped image if you mount, with foam specifically. The foam gives just enough to enable you to get a clean stamped image...which is what we want, right?
I always mount my stamps on 6mm craft foam. I like to get the neutral colors from Stampeaz, but when I run out I resort to the black, white and red available from my local craft store.
I always recommend Perfect Glue #1 (by Liquid Nails). It sets quickly, has low fumes and is fairly flexible. The only thing I don't like about Perfect Glue is the cap on the tube; poor design, in my view. To solve this problem, I insert the tube into a zip bag and put on the cap over the plastic bag. This way it seals the tube better than the cap alone.
For smaller stamps, you all know that I have used the AQ pencils as a mount. Very fun, but what about when you run out of those cute little pencils or your stamp is a little bigger? I have been using baking clay with great success; you can mold it just as you like and just bake it for a bit, and voile!...custom mount. For such small stamps, I don't use foam and they seem to stamp alright.
I have found the best glue for attaching the carving material to the baked clay is 3-in-1. It does have a bit of a smell (that does diminish as it cures) and it is a bit stringy, but it holds great and sets quickly.
I would like to discourage mounting on hard materials like wood, tile or plexi-glass without foam. It is so frustrating to try to stamp a wonderfully carved stamp that is mounted to these materials, and not be able to get a good, clean image due to the inflexibility of the mounting. If you must mount on these things, just use a little bit of craft foam in between the carved stamp and the mounting; the 3mm or 4mm foam will go a long way to giving cleaner stamped images.
If you have any other great ideas for mounting, or would like to share how you mount and finish your stamps, please leave a comment - I'd love to hear them!