Me too - double sided carpet tape. I use it to keep 2 mats together side by side, to double my cutting surface.

Double sided tape made by "gorrila glue". You don't need much - just along the sides.

I've used double sided tape in the past for the smaller blue one and it held for a little while, but not too long. The blue one is on a folding table, like the kind you buy at Wal-Mart, and the large mat is on a slick surface, like a laminate counter top.

Oh, I hadn't thought of the Gorilla Glue Tape! That might work perfectly. Where would I find it? I haven't seen the GG Double Sided Tape before.

Binder clips or alligator clamps, whichever is closest and fits best on the table. My setup has to be modular, so I can't use any kind of adhesive.

I bought this at either Home Depot or Lowe's. You might be able to find it at Walmart tho. It's great stuff!! :)

In my classroom we use this tacky blue stuff so students don't slip out of their chairs and to hold adaptive writing surfaces in place. We get it from the occupational and physical therapists, but I have no clue what it's called. It's thin, and really floppy. Probably silicone or something similar. I bet it would work great for this purpose. I will go hunting for it...

I have a 23x72 cutting mat and it's in two pieces. It's held together by a clamp on both ends that has 2 screws on each end. Every so often I have to check the screws because they become loose. Ask at your local quilt store if they can order just the parts I'm talking about. The clamps are gold colored and slide on. Then you put the gold colored screws in the holes and just tighten them with your fingers. I know you can order them separately, because I accidentally lost a screw because I wasn't paying attention and one came loose and fell off and I couldn't find it. Maybe google 23x72 cutting mat. I just looked at it and it's called an "Olfa Mat Clip". Hope that helps.

Thanks for all the great suggestions! I don't know if I can easily screw into the table that it's on, but I like the idea of clamps, perhaps with superglue?? First, I'll try the double sided Gorilla Glue Tape, though. Thanks!

I use double-sided tape too. I have two 24x36 mats butted together to make a large mat. They've been stuck in place for a couple of years now with no slipping...