Depletion lands are nonbasic lands that enter the battlefield with a number of depletion counters (or another type of counter) on them and can be tapped and counters can be removed to add mana. In contrast to storage lands, additional counters cannot be added to these card by themselves at a later point in time, so the mana source runs out with use.
Ice Age depletion lands
The "depletion lands" from Ice Age introduced depletion counters, but are much closer to slow lands functionality wise. Each land could be tapped for one mana of an allied-color pair and the land would gain a depletion counter, which would be removed at the beginning of the land's controller's upkeep and which would prevent the land from untapping as long as it had a depletion counter on it.
Weatherlight introduced the first true depletion land. Gemstone Mine enters the battlefield with three mining counters. It can add one mana of any color for and the removal of a mining counter. When the last counter is removed, it is sacrificed.
Mercadian Masques depletion lands
Mercadian Masques introduced a cycle of depletion taplands. Each of these lands enters the battlefield with two depletion counters. Each can add two mana of a specific color for and the removal of a depletion counter. When the last counter is removed, the land is sacrificed.
Tendo Ice Bridge
Introduced in Betrayers of Kamigawa the Tendo Ice Bridge enters the battlefield with one charge counter on it and can be tapped for . It can also add one mana of any color for and the removal of a charge counter.
The vivid lands are taplands introduced in Lorwyn. They enter the battlefield with two charge counters on them. Each can be tapped to add mana of a specific color. They can also remove a charge counter from them to add one mana of any color.
The artwork of the vivid lands depicts a location associated with their specific color, and a rainbow which is a theme often used for cards which can produce any color of mana.