Dual Lands - are possibly the most famous and sought after nonbasic lands in Magic. Printed in Alpha, Beta and Revised, all 10 of the lands count as two different basic land types. Due to an error, Volcanic Island was not included in Alpha, but was included in Beta and Revised.
Pain Lands - originally printed in Ice Age and only with ally color combinations. They allowed you to tap for colorless mana normally or one of two colors by taking 1 damage. After Ice Age these were reprinted in 5th, 6th, 7th, 9th and 10th edition. The enemy color combinations were first attempted in Tempest, but the lands came into play tapped and were not popular. Versions that came into play untapped were seen first in Apocalypse, a set with an enemy colored theme. The enemy lands were reprinted in 9th and 10th edition along with the originals.
Filter Lands - a set of ally color combination lands from Odyssey. The enemy combination lands were never made. The signets from the original Ravnica worked similar to the filter lands, but were artifacts instead of lands. In Futuresight a future shifted land was similar to the original filter lands using hybrid mana instead of colorless. All 10 of the hybrid filter lands were later printed in Shadowmoor block, allied in Shadowmoor and enemy in Eventide.
Fetch Lands - a staple of tournament play, fetch lands allow you to tap, pay 1 life and retrieve one of two basic land types from your library. The thing that makes them useful is the fact that the new land comes into play untapped. The original fetch lands are actually from Mirage and did not require the 1 life, but they came into play tapped and thus delayed you a turn. Only the allied color combinations were printed for the original Mirage fetch lands. The new fetch lands were printed in Onslaught, with enemy color fetch lands printed in Zendikar. Since the Onslaught fetch lands were printed prior Mirrodin we may see them reprinted in the next couple years for Modern format.
Shock Lands - printed in Ravnica and reprinted in Return to Ravnica. These lands finally gave a new dual land that has the basic land types, allowing great interactions with fetch lands. Shock lands get their name from the spell Shock, which does two damage. When shock lands come into play they are tapped unless you take two damage. The shock lands were deliberately given generic sounding names so they could be reprinted in any set, not just one on Ravnica. Funny, since they actually were reprinted in another Ravnica set.
Bounce Lands - also called the Karoo Lands after a cycle of lands from Visions. The Visions lands required you to bounce a specific basic land type and would tap for that color plus one colorless. The guild bounce lands printed in Ravnica all tap for two mana of one of the ten combinations. Printed at common level as a mana fix for limited, the bounce lands do not entirely fit with current printing rules. The mechanic is a little too complicated for common and they are also a little too good for common. They would probably be reprinted as uncommon if they are ever reprinted.
Tap Lands - also called the M10 lands, since tap lands can refer to many land cycles. First printed in M10 then in M11, M12 and M13 with allied colors. These come into play tapped, unless you control a basic land for one of their colors. Enemy colors printed in Innistrad. Get your playsets now because Maro has hinted they will not be printed in M14.
Fast Land - one of the newest land cycles, also called Scar lands for the set they were first in. These lands come into play untapped only if you don’t have a lot of land. Only the allied lands exist, we’re sure to see enemy color versions someday.
Gates - gates are merely the most recent version of these cards. In Invasion allied color uncommon lands that came into play tapped, but allowed for two mana production were seen and these were reprinted in 8th edition taking the place of the Pain Lands. In Coldsnap functional reprints were seen again, but this time they counted as snow lands, again only allied colors. Once Shards of Alara came out though, versions of these lands were printed that could tap for 3 colors and the two color versions needed to be stepped up a little. In Zendikar, the Refuges were printed, allied color and you gained 1 life when they came into play. Finally in Return to Ravnica we got the Gates. Gates are the first of these type of cards to be printed at common and the first cycle where allied and enemy combinations were printed. Gates interact with a handful of other cards, usually making a creature a little better.