Fora and forums are plurals of forum. The former conforms to the original Latin, which some people prefer, while others like the Anglicized form. Neither is right or wrong, and choosing between them is mostly a matter of preference. Be aware, however, that forums is by far the more common form in most types of writing throughout the English-speaking world. Fora still has the edge in scientific and scholarly contexts, though. This is not surprising, as Latin forms are typically more common in these types of writing. Outside these contexts, fora can be distracting and even confusing to readers who are used to seeing the English word.
Of course, there are some Latin plurals conventionally used in English even outside science and scholarly writing. Memoranda, for instance, is more common than memorandums, and phenomena is considered the only correct plural of phenomenon. Fora is not among these, though. It is clear that most English speakers prefer to pluralize this word in the English manner.
Frequency of use
In British newswriting from this century, forums appears about ten times for every instance of fora. The ratio is closer to 100:1 in U.S. news publications, and it is somewhere in the middle in searches covering Canada, Australia, and New Zealand. In a search covering a few dozen of the most popular blogs from throughout the English-speaking world, the ratio is almost 1,000:1.
The picture is much different in searches covering books, magazines, and journals from this century. Here, fora is still nearly as common as forums, which is not surprising because these searches cover a lot of scientific and otherwise scholarly texts. Only in searches exclusively covering scholarly articles from this century (via Google Scholar) is fora more common, by a ratio of about 3:2.
Below is an ngram, courtesy of Google Books, graphing the use of fora and forums in a large selection of English-language books, magazines, and journals published between 1800 and 2000. It shows forums slowly gaining ground before prevailing in the middle of the 20th century:
Fora is almost nowhere to be found in publications and websites such as these:
The latest controversy surrounds Reddit, a community and social news site that lets members create and run their own forums on any topic. [New York Times]
The aim now is to give the funding to local forums to develop a local plan for their area. [Guardian]
If requiring people to use their real name helps cut down on the amount of utter nonsense that goes on in those forums … so be it. [TechCrunch]
In a video released by the SITE Intelligence Group on jihadist forums and translated by the US monitoring service, Zawahiri also lashed out at US President Barack Obama. [Mail & Guardian Online]
According to a new analysis of 18 hacker forums from around the world, the answer often is: your Facebook and Twitter accounts. [Bloomberg]
This year’s five-day conference began on Thursday and a series of open forums are slated for Saturday. [The Australian]
But if you know where to look, it’s easy to find instances of fora still used in this century:
We extend our thanks to the participants of those fora. [International Journal of Law in Context]
Multilateral fora are the subject of a paradoxical situation where the benefits for participant states increase as membership nears universality, while at the same time the flexibility and decision-taking capacity of such fora decreases. [The European Union and Interregionalism, Matthew Doidge (2011)]
Nation-states are constitutive building blocks in global fora. They are what such fora consist of and are active agents in them. [The Sociology of Globalization, Luke Martell (2010)]