LEGO-compatible suction cups?
From the post about Vertigo (the precursor to Rory's answer), TrilogyGlenIvy (the creator) stated:


  Suction cup hangers were easily located in stores. Drilling a small hole and inserting a short section of copper tubing (1/8 “ or ~3 mm diameter) along with some vinyl glue produced the feet that I used.


Basically they are usually found in DIY/Home stores as metal or plastic hooks wrapped around a transparent suction cup so you can easily affix them to tiles or windows.

There is also a picture showing three variants that were tried, with the preferred option being those in the bottom left I think:



Depending on the weight of the model you've got you may also need to invest in some additional custom air bellows:


  An internet search finally pointed to a “Climb@tron Vertibug” toy that contained two air bellows (~23 mm in diameter). I bought one of the toys, removed the air bellows, and designed a “worm gear slider” system using NXT parts to stretch and compress them. The vacuum system was then installed in Vertigo and has worked reasonably well.