Forum has three main meanings. There is the everyday sense — a place or medium for public discussion and the open exchange of ideas; the legal sense — a court of law, tribunal, or other legal assembly; and the historical sense — a marketplace or other public arena in ancient Roman cities, where civic, commercial and judicial activities were conducted.
The first sense includes online discussion forums. Several of these have featured discussions about the correct plural of forum itself — is it forums or fora? — as have some language blogs and other sites. Latin plurals are evidently a popular topic. Some of the commentary is sensible and even-handed, but some comprises simple repudiation of one plural form or the other (e.g. ‘The plural of “forum” is… FORA since it’s a Latin word. […] Sorry to be pedantic, but that’s the English language for you’), so a little clarification seems to be in order.
Forums reflects the word’s naturalisation into English, while fora stays true to its Latin origin. Forums is much more common, outnumbering fora by a considerable margin. This is especially so in the word’s everyday sense; in its legal and historical senses, fora is less unusual. (I’ve based these assessments on personal reading and editing experience, and on searches in various corpora and search engines; I would welcome a more rigorous contextual breakdown.)
Fora in the everyday sense of forum is not incorrect, but some readers might find it fussy or pretentious, and usage commentators disagree over its suitability. Don Watson considers it “archaic”. All three editions of Fowler’s report that the plural occurs only as forums. (This, however, is demonstrably wrong.) Kenneth G. Wilson, in The Columbia Guide to Standard American English, lists both forms as standard. Bryan Garner takes an intermediate position, describing forums as “preferred” and fora as “pedantic”. So it’s fair to conclude that this is a grey area.
The English language is inconsistent in its pluralisation of Latin words. Of those ending in -um, some retain the Latin endings (bacterium → bacteria; quantum → quanta; stratum → strata; ovum → ova; desideratum → desiderata); others, being more Anglicised, generally take the English -s (albums, asylums, museums, gymnasiums, crematoriums, premiums); while some commonly take either, depending on context or personal preference (atriums or atria; aquariums or aquaria; compendiums or compendia; podiums or podia).
In summary: fora is not wrong, but unless you’re writing about law or Roman history, you’re better off using forums. Foras is wrong.
See also: Data is data, or are they?