A recent paper (available as a pdf file) by Vincent Hayward in Brain Research Bulletin lists more than twenty types of tactile illusions that can be experienced using very simple equipment available in any hardware store. Some of the descriptions of the illusions unfortunately are rather technical, but here's a summary of a few of them:
The Aristotle Illusion: Cross your fingers and touch your nose. You may feel two noses. (It didn't work for me.)
The Comb Illusion: Lay your finger on top of the teeth of a comb. With your other hand, run a pencil back and forth against the teeth. You should feel "the sensation of a raised object moving on the finger when, in fact, since the teeth have a constant length, the skin is sheared but indentation is invariant along the line."
The Curved Plate Illusion: Move a plastic card or match box back and forth across the pad of your finger. It should feel straight. But if you see-saw the object up and down as you move it across your finger, it should feel curved.