Although the traditional answer to this question is 'two', some records even have fewer than two grooves. Test pressings of albums and singles, either vinyl
or some other less durable material, are often created as a double-disc set, with one side of each disc being blank
, as it is quicker and easier to press a single side of a record twice than to press two sides of a single record. Furthermore, artists on a stritch budget at a time when vinyl was prevalent could pay for a single-sided pressing, and some DJs nowadays prefer single-sided records for reasons outlined in one-sided LP
So, a record can have anything from one to a potentially infinite number of grooves. If a record has no grooves, it's not a record, it's just a plastic disc, or an object d'art of the kind produced by Project Dark. Having said that, the question 'is a record without a groove still a record?' is the kind of thing one might be asked when applying for a philosophy degree at Cambridge University.
The most famous multi-groove record is probably Monty Python's 1973 LP 'Matching Tie & Handkerchief', which had a double groove on side two, although only the original vinyl pressing included this feature. Subsequent reissues (and editions on cassette and compact disc) simply ran the two sides twos sequentially.
Another clever vinyl trick is the endless groove, a loop which doesn't spiral into the run-off area and could presumably cause havoc with a jukebox, if a single was to feature such a thing; Peter Gabriel's 'Peter Gabriel' features one of these, as did Lou Reed's 'Metal Machine Music'. As far as I know no-one has yet released a single consisting of a single circular ring etched in the vinyl, although Napalm Death have produced songs short enough to fit (the classic being 'You Suffer'). Multiple locked grooves are popular in the techno world, and both Speedy J's 'Loudboxer' and Richie Hawtin's 'DE9: Closer to the Edit' were released in locked-groove forms (both albums boasting over 200 tracks, presumably of great interest to DJs and/or remixers).
Thanks to sneff, mkb and enth for the information in the last paragraph.