What would cause a 1991 Honda Accord to shake in reverse?

I am assuming you have an automatic transmission in your 1991 Honda? The 'vibration' you describe is likely due to worn motor mounts/shock absorbers. These Hondas have three different motor mount brackets, each of which has a rubber vibration-isolating bumper in the mounting assembly. I replaced the ones in my 1992 Accord EX (auto transmission) and it definitely solved the problem. It's not as big a problem to fix as it may sound like, but may not be something you want to tackle by yourself if your are not mechanically-inclined. These parts, from HOnda, will be extremely pricey. I purchased my motor mount brackets by searching on eBay, and saved a considereable sum of money, and I coulnd't see any appreciable difference in quality. Check the engine and transmission mounts.