Time Lords themselves are able to live to advanced ages, several hundred years; additionally, when they die, either of natural causes or from violence or illness, they are able to regenerate into a new body, with all the memories of the old one but a new personality. Time Lords can regenerate up to twelve times before they finally die; there are a few exceptions to this rule, such as extermination by a Dalek (unless Uncle Rusty's at the helm), specific Time Lord technology, in which case they die for good, or having a new cycle of regenerations bestowed upon them. Regeneration can be interrupted, which also results in permanent death for the Time Lord.
The Doctor is perhaps the best known Time Lord, and is currently in his fourteenth regeneration. While in his ninth regeneration, he was known as the War Doctor and took part in the Last Great Time War during which Gallifrey, home of the Time Lords, was destroyed, along with most of the Time Lords themselves. It was later revealed that the Time Lords were burnt out of existence by the Doctor himself: after years of fighting, he reasoned that the mutual destruction of his people and the Daleks was the only way to put an end to the horrors of the Time War.
Despite this, both the Doctor and the Master survived.
Not all is lost for the Time Lords, however; the Tenth and Eleventh Doctors managed to change their personal timelines by travelling to the past and helping the War Doctor to conceal Gallifrey in a pocket universe. While the Time Lords have been spared from destruction, their planet is still lost in another dimension, waiting for the Doctor to find them and bring them back to the universe safely. The downside, of course, is that bringing the Time Lords back would instantly restart the Time War.
The standard Time Lord disguise includes a complete regeneration cycle, a fact some agents have exploited to cheat death.
Additionally, multiple Time Lords are known to have survived by being in the PPC at the time.