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Does anyone know any cheap tools are free techniques for cutting regular holes in plastic sheet? I’m talking about holes larger than what you would get with a drill. I know routers exist but I am not going to invest in one for a few holes.

Cheers Vim

A couple of options:

Use a nail, some string and a sharp scalpel blade to get a nice scored circle then break that out, or what I do is I have a compass with a pair of points in it and score the circle that way. I've also taken to doing something the same again with my calipers, but I have to take care with it that way.

Buy one of these:

http://www.amazon.com/SE-791LP-Heavy-Duty-12-Piece-Hollow/dp/B000KE17JO/ref=sr_1_1?ie=UTF8&qid=1370615841&sr=8-1&keywords=hollow+punch

You want a reamer, only a few euro's

This is what I use
http://www.ebay.co.uk/itm/Model-Craft-Tapered-Reamer-with-Hand-Grip-16mm-PDR0075-/400479480026?pt=UK_ToysGames_ModelKits_ModelKits_JN&hash=item5d3e6fe8da
make a hole in the plastic and then keep twisting till you get to the desired size.

How thick plastic sheet? How big of holes?
Several of the solutions here will work, some better than others depending on the thickness.

For thin stuff, most of the crafting circle cutters will work.