On a CRT monitor, yes. On an LCD monitor, no. Also, I found that certain CRT tubes don't like being turned on one of the sides, whereas the other side seems fine.
All colour TV sets have some sort of degaussing coil, no matter how old - they might just take a while to work. If you get crazy colours (and by the way it'll make it worse if you tate it while it's turned on!), turn the set off (by the main power button) for about 10-20 minutes (maybe longer) - you may even need to unplug it depending on the model. When you turn it back on it should have improved - you can try again if it's not good enough though. I tried this with a Sony 21" from the late '80s and it was fine after leaving it off for 10 minutes - well it was as good as it was gonna get, as the colour was already fuckered down one side ^_^ Decent modern TVs will have a proper degausser that'll go on every time you turn on the TV - if it makes a big clicky noise when you switch it on that'll be it. A lot of TVs now even do it when they come out of standby.
It all depends on the TV/monitor. If the CRT monitor has a degauss feature (which many due) that is a great start.
my dentist used to have 17" CRT TV fixed into the ceiling so when you lying on the chair you can watch the telly above you - they changed it with LCD one recent time but for those 7-8 years didn't see anything happened to it... fwiw...
I'd just reccomend picking up an old arcade monitor. Look in your phone book under amusements. I bought a used 19" vert monitor for $35 from a local shop about 2 years ago because the one in my Arkanoid machine decided to shit out on me. Shouldn't be more than an hour of work to build a frame and box out of wood to go around it and then you'll be able to play on a real arcade monitor instead of a tv. Plus, you can just lay it on its side and have a horizontal monitor for your other games!
