I was recently very lucky at a local (French) charity shop - Emmaus: I bought a nice bike for €15. Surprisingly nice: quite good quality equipment, but everything on it could be dated to no later than 1988 (original Shimano Deore RD MT 60 rear derailleur, for example, with letters for January 1988). It appears to have been used only once or twice - no wear at all on the brake blocks.
The tyres, however, are presumably 25 years old too. They were flat when I bought the bike, but I've pumped them up hard and they have stayed that way. They are Michelin Select 700 x 23C tyes and they do show a bit of cracking, though not a lot.
Should I just use the existing tyres until they actually let me down, or would it be a lot safer to replace them almost at once?