Suicide buttons exist in most FPS games I've ever played. Oh the hilarity inherent to binding someone's shotgun key to suicide while they pop off to the bathroom in quake 3.
Depending upon the game, there may be a compelling reason. In Team Fortress, dying is the only way to switch classes for example or in a massive game like Tribes, a suicide is the quickest way to get back to your base if you're really in a hurry (and, given that you might be several kilometers away, that could save you several minutes of travel time).
Other games have used the Suicide as a game mechanic. Tribes Renegades featured a suicide det pack as a backpack item for one of the classes. It made outright winning any battle with another player all but impossible but it was the games equivalent of a thermonuclear device. Simply put, if you had a line of sight to the thing when it went off, you were probably going to die. It was useful as Renegades allowed the defending players the ability to build enormously complex defensive systems with overlapping force fields and unholy levels of firepower that would take nearly endless quantities of ammunition to punch through normally. A suicide det pack offered one player the ability to put a very deep dent in such defenses quickly, assuming they could even make it deep enough into a base for it to matter. Basically, you had two ways to detonate the device: you could set it down and wait for 20 seconds (where it could be defused if I recall correctly), or you could simply commit suicide and it would go off instantly. On one occassion, when trying to make my way to the enemy base, I found myself facing an assault force on the ridge just in front of our own. In the time it took to climb the hill to help join in the defense, a full HPC of reinforcements was moving in. So, realizing that without an energy pack I wasn't going to be useful anyhow, I just flew to the appropiate height and just before I was run over by the HPC I killed myself, taking the passengers of the HPC, the bulk of the attackers on the ridge proper, and, after more than a minute, the pilot of the HPC as well (he survived the blast but was propelled over a kilometer into the stratosphere. He did not survive the landing).
Most games still give the kill to an enemy when you commit suicide in some form or fashion, and even when they don't it still can prove a useful enough tactic. When playing on the famous DM17 from Quake 3, if your opponent was one kill from victory and you were engaged in a combat where you would likely win, jumping off the ledge to your death was a sounds strategic move. It certainly made it more difficult to win, but it at least kept the possibility of victory open.