Anything can be a classic. If you check the Photo Galleries section of this site you will see a few photos from the National Fork Truck Heritage Centre (it sounds a lot bigger than it is). Though I don't think there is a large market for classic lift trucks, obviously there are some collectors. Surprisingly you can still find lift trucks from the 40s and 50s still being used (often in small shops or really old manufacturing facilities). From a safety perspective, I'd rather see somone fixing these up for display rather than people still using them. There are little bits of forklift history scattered around the internet. Unfortunately the linking policy of fokliftaction doesn't allow links but you can do some web searches and check out some of the older lift truck manufacturer sites (they sometimes have a history section).
If you're asking this question because you think you can make money off of old lift trucks, I think that's probably a long shot, but if you're just interested in restoring some old trucks because you like old forklifts, go for it.