The accepted definition of vintage guitars is anything over 25 years, so frightenly (well for those of us who started playing in the 80s!!), 80's guitars are now starting to be considered vintage.
Interest in old guitars started when people wanted models that were no longer production (if you wanted a Les Paul in 1965 it would have to be 2nd hand), when specs changed, or production quality nosedived.
Most people when considering vintage instruments focus solely on the usual suspects ('bursts, 50s Strats/ Teles etc), see the astronomical prices and conclude that vintage instruments aren't worth bothering with.
However, there are plenty of great value quality vintage instruments, which are often cheaper than a modern equivalent.
For example you can get a straight 60's Guild Starfire IV or V for less than the price of a new Gibson ES-335.
60's Gretschs are good value too when compared with the modern reissues.
I often gig with a 50's Gibson ES-225T. Not everyones cup of tea, but a beautifully made instrument, which cost me about the same as a 2nd hand ES-135 (it's nearest modern equvilant).
Vintage accoustics can be very good value.
Vintage amps can also be very good value, and are often less than the price of a reissue.