I'm sure that if you've gotten this far in this thread, you know that plexiglas (acrylic plastic) is not a good structural material. What might be missed is why you would use one material over another, and how you'd choose the "best" one for your application.
[A little disclaimer here: I am not a mechanical engineer or materials expert - but I do have a tattered degree from the school of hard knocks.]
First - the term "plastic" tells you something right off about these materials: they can deform, move, flow and/or creep by nature. This may be a good thing if you want low friction, impact resistance or high toughness. It also means that in general, their strength may not be the greatest. (There are exceptions to every rule, but we're talking generalities here.)
So, going back to a couple of plastic materials mentioned in this thread, what's so good or bad about acrylic and polycarbonate? Acrylic is great for clarity - you can polish it so it looks like crystal glass. It has pretty good machineability with the right tooling, too, but those tools require a different profile than what you use for metal or wood. It is pretty hard and stiff, but does break easily (notice I compared it with glass earlier). Personally, I really like working with the stuff, but I can't think of anywhere I'd use it on a robot!
Polycarbonate is what they make bullet-proof windows and jet canopies out of. You can
bounce a chicken off it at very high speeds. Or another robot at somewhat lower speed. Great flexibility, too, in thin sections. Not so nice to machine, as it tends to grab the cutter and needs coolant to keep from melting, but sheets can be sheared and bent just like sheetmetal. You shouldn't expect holes tapped in it to hold a lot of force, either in tension or shear - use through bolts, nuts and washers. So this is good stuff for the bumpers, feelers, side covers and things that go bump on a robot.
Polyethylene (HDPE, UHMW, LDPE) is great as a sacrificial wearing surface, chain guides for example, and for chemical resistance. It's okay for lightly loaded bearings, but it's a pretty lousy structural material.
One way to look at materials for structures (like robot frames) is their strength to weight ratio. If we compare the ultimate tensile strenght divided by the density we get a picture of why people use steel for fasteners and really strong structures, aluminum for weight-sensitive structures, and plastics for the rest. (The numbers are the ratio of the UTS, in MPa, to Density, in g/cm3)
ASTM A574 Steel: 160
6061 Aluminum: 122
Polycarbonate: 58
Acrylic: 51
Delrin: 48
HDPE: 29
Teflon: 14
[End of lecture]