Had hazed over headlight covers and thought to get them replaced: until informed of their cost. However, told that they can be restored. Auto parts stores sell a kit for restoring hazy headlight covers. Was told that the outer layer of the clear plastic becomes deteriorated over time through exposure to sunlight, ie UV radiation. Restoring takes some time, process, and manual labor; the kit about $40. The deteriorated plastic is sanded away, remaining clear plastic is smoothed, and a filler/sealant is repeatedly applied and polished. Worked well for me: result are clear, sparkling looking headlights that emit significantly more light. Once restored, one realizes how much light has been lost. The appearance of the car is improved - no more car with cataracts - and most important, for safety, the lights are returned to their designed level of function. It needs to be done; one sees so many cars with deteriorated headlight covers. Have not researched, but one could expect some body shops, glass shops, or even auto detailers to be able to do it. Think it is worth it. By the way, if one has a new vehicle with plastic headlight covers, it is just a matter of time: shorter if parked in the sun. However, there is an auto finish product I got talked into (by same store that talked me into getting the headlight restoring kit) that I suspect contains the same substance the kit has for the final seal and polish. Will not of course reveal the brand name here, but the name contains a word I used here (places that might restore headlights). This product claims to protect the finish from UV damage, so using it on the headlights (which seems to polish them up) could protect them from the problem of deterioration haze.
For less than $40 you can buff the lens with the stuff used for cleaning ceramic stove tops. Worked on my '96 Ranger. If the lens is polycarbonate avoid anything that contains any acetone.
On the show, Click & Clack said the cost of replacement is very high. You can go online or visit your local auto recycler to obtain this part for small money - $40 to $45 for the whole '96 Ranger headlight assembly in my area. These parts function as good as new and carry a full replacement warranty. We could all profit from utilizing recyclers!
If everyone who has this problem would contact their political representatives and tell they (and the car manufacturers) you want to go back to glass that would never have that problem and cost far less.
Well, I’ll name a product that has worked great for me - Meguiar’s Plastix. It cost me $3 for a bottle at the local parts store that has lasted near 5 years with 2 cars getting the occasional polish. Freakishly good results with amazingly little work.
Some other people have posted pictures of their results here:
The effect on that Civic Si is simply stunning. Some people say you can get the same effect with toothpaste, but that’s probably no cheaper than what the Plastix cost me. 
The PlastX works on other things too. The door on my dishwasher is a black plastic sheet, and no matter how much we cleaned it, it would look hazy and dirty. 2 minutes with the PlastX and it was shinier than new (and lasted a year and counting so far)
My dealers service department suggested I sand with water and emery cloth. Afterwards I sprayed with a clear enamel that would not harm plastic, (local hobby shop). It worked for the entire winter but it is something that should be done yearly.
I had a fender bender a while back - '05 Prius, and as part of the repair they buffed the headlight. For $70 I had the other one buffed. It made a great difference in the light output. But I think I’ll try the PlastX myself next time.
Absolutely! Those things can be sanded/buffed & made good as new! Just be sure to wax 'em from time to time.