You're thinking... hey, it's the Plastic Genius, there must be a solution to this! Well, there is and here's the basic idea.
1. Stop the crack NOW. You do this by drilling a teeny hole at the end of the crack. Teeny will be defined as the smallest drill bit you have laying around. From 1/16" to 1/8" will work fine. You don't need the special Plexiglas drill bit for this one since the Plexiglas is already cracked. (otherwise, you really DO need those bits for NEW holes).
2. The hole drilled at the end of the crack will STOP the crack from propagating any further. Depending on the severity of the crack, this might be all you need. I had a patio table top that cracked in 2000 when the wind blew over the table and the umbrella pole jammed the hole. I had a 3 inch crack. Drilled a 1/8" hole in it. With a metal drill bit. I finally replaced the top last summer in 2008. Not because I wanted to, but I was getting grief from my wife about having a plastics company and I really had no excuses left - 8 years was a solid test of my fix.
3. Filling in the crack. This is tricky AND you may have some success if this is a display case, window, or other stationary object. The water thin adhesives such as WeldOn #4 will "wick" into the crack by capillary action, and probably spill out around the crack (wipe off with Kleenex quickly). I generally do not recommend. If there is vibration (like a camper window) it will open up again - but the crack will not get longer.
4. Airplanes, gliders, and other aerospace cracking. Drill a hole. Normally, the plexiglass acrylic used in plane windows and windshields is different than the plexiglass used in displays and windows. It's chemical resistant and the regular #4 glue won't work. It may or may not be "stretched" or "pre-shrunk" acrylic. I don't know FAA regs, but I doubt slapping on a strip over the hole will pass inspection. However, that said, you "could" do that by using another glue such as WeldOn #16 or better, WeldOn #40 and a small piece of CAST plexiglass sheet (not extruded).
5. Preventing Cracks. Most cracks propagate from holes or from edges that have not been smoothed after cutting. When you get plexiglass from a "real" dealer (not HD or Lowes) they have the equipment to cut sheet correctly. When you DIY, you might have some chips from your cutting. That's OK - just sand down the chips with 80-100 grit sandpaper. Trust me on this - it makes ALL the difference in the impact resistance of the final piece. BTW, the same goes with polycarbonate (Lexan) - it is also "notch sensitive" (like glass too) and WILL break at the chip. Now a lot of cracks come from the HOLE that was drilled. First - make sure you use a Plexiglas drill bit (the head is reshaped to a 60 degree angle and carves through - metal bits punch out the backside of the plexi and cause chipping). Second - make sure the hole is BIGGER than the screw or bolt. Why? The expansion and contraction of the plexiglass will put stress on the hole. Overstressing causes cracking. This can also happen in a window where something impacts against it - and Boom, there's a crack in your sheet. According to Cyro Industries (Evonik): When drilling holes to support sheet by point fastening, there are two rules that apply. First, the bolt hole diameter should be at least 2 times the diameter of the bolt. This allows for adequate clearance for thermal and moisture expansion and contraction. Second, the distance from the hole center to the edge of the sheet should be at least 1.5 times the diameter of the drilled hole. Please see the picture below for a detailed diagram.
6. Preventing Cracks - Part 2 - while we are on the discussion of holes, try NOT to countersink. Countersinking basically STOPS the ability of the sheet to move. This causes cracking. It is always best to drill a hole slightly larger than the bolt or pan-headed screw and use a washer to disperse the energy of an impact. That said, NEVER tighten a bolt or screw "all the way". Hand tighten and then back off 1/4 turn. This allows for expansion and contraction too.
Attention Boat Owners: I know, you have to countersink that 1/2" thick hatch cover with screws every 5". But the difference is you are also using a flexible sealant underneath, and impact is usually in the form of a wave which spreads the energy. Don't forget to back off 1/4 turn though.