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I haven't played Magic: the Gathering since the days of Onslaught and Mirrodin, and I would like to try to catch back up. Since all my cards are quite dated now, I may be more interested in formats other than the most up-to-date one.
Rather than ask what is currently legal in various formats (since that is likely too localized), I would rather pose the question of how can I tell which sets/cards are legal in each format.
I would refer you to the following page:
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/formats
I think you'll find everything you need there! Both lists of legal sets for each format, and lists of individual cards that are banned or restricted in those formats.
There are six constructed formats, and although Wizards doesn't have a good reference to how/why sets rotate into and out of formats, Wikipedia does a good job of enumerating them, and describing what sets are legal for each format. As to the banning of individual cards within a format, Wizards Banned/Restricted list for each format is continually updated.
Vintage - The Vintage format, formerly known as Type 1, allows cards from all sets that are legal for constructed play (known as an "Eternal" format). Vintage maintains a small banned list and a larger restricted list. Unlike in the other formats, the DCI does not ban cards in Vintage for power level reasons. Rather, banned cards in Vintage are those that involve ante, manual dexterity (e.g. – Chaos Orb), or subgames (e.g. – Shahrazad). Cards that raise power level concerns are instead restricted to one per deck. Vintage is currently the only format in which cards are restricted.
Legacy - Legacy is another "Eternal" constructed format. It also allows cards from all legal sets, but unlike Vintage, it maintains only a banned list, and cards are banned in Legacy for power level reasons. The format evolved from Type 1.5, which allowed cards from all sets and maintained a banned list corresponding to Vintage: all cards banned or restricted cards in the old Type 1 were banned in Type 1.5. The modern Legacy format began in 2004, as the DCI separated Legacy's banned list from Vintage and banned many new cards to reduce the power level of the format.
Modern - Modern is the newest constructed format. Modern was created by Wizards of the Coast in the Spring of 2011 as a response to the increasing popularity of the Legacy format, which although popular proved difficult to access due to the high price of staple cards. [...] Modern allows cards from the 8th Edition core set and all expansion printed afterwards. The 8th Edition core set was when Magic cards began to be printed in modern card frames, and this is where the name for the format is derived. Wizards believed this cutoff would have the advantage of giving a visual cue as to which cards are legal in the Modern format.
Extended - The Extended format, formerly known as Type 1.x, consists of the last four years' of blocks and core sets. With each autumn set release, one year's worth of sets rotate out of the format. Any additional sets released between rotations are automatically added to this format's card pool. The format previously contained seven years' of blocks and core sets. The new system was implemented in July 2010 to reduce the format's card pool, with the intention that this would make the format more understandable and attractive to play.
Standard - The Standard format is continually one of the most popular formats in the constructed deck tournament scene. It is the format most commonly found at Friday Night Magic tournaments, played weekly at many hobby shops. Standard used to be referred to alternatively as "Type 2". While the name, "Type 2" has been dropped officially, it is still commonplace that the standard format be referred to this way. This format consists of the most recent "Core Set" release and the two most recent "Block" releases, with one exception. "Rotation" occurs every fall when the first set of the new "Block" releases and becomes Standard Legal. From the time the new "Core Set" is released in early summer, until rotation occurs, 2 core sets are legal.
Block Constructed - The Block Constructed format uses only the cards from a single block of Magic sets. Magic sets since Mirage have come in groups (usually of three) known as blocks. Block Constructed formats, and blocks themselves, usually take the name of the first set in the block. For example, the Ravnica Block Constructed format consists of Ravnica: City of Guilds, Guildpact, and Dissension. Only cards that were printed in the sets in the appropriate block can be used in Block Constructed formats.
As an update to other answers, Standard has changed to include the last 3 blocks of 2 sets, instead of 2 blocks of 3 sets. In addition, as core sets are no longer to be released, the blocks are changing from 5-8 sets to 5-6.
So basically, the old standard was (with a few exceptions):
The new standard will be:
As a special case, during the transition, the Tarkir block is being split up:
You can use Wizards of the Coast's Gatherer Website to generate lists of cards for each format.
For example, here is a list of cards legal in Standard Constructed.
