Obi-Wan Kenobi is a primary character in the Star Wars continuum, and one of the few characters to appear in all six films. He is portrayed by Ewan McGregor (as a young man; prequel trilogy) and Alec Guiness (as an old man; classic trilogy).
Raised in the Jedi temple, Obi-Wan was trained by Master Qui-Gon Jinn until Qui-Gon's death, at which point Obi-Wan took on Anakin Skywalker as his own apprentice, in accordance with Qui-Gon's wishes. For the next twelve years, he and Anakin grew to be good friends, "like brothers," both becoming generals in the Clone Wars and leading troops to victory against the Trade Federation.
When Anakin turned to the Dark Side and became a Sith Lord, Obi-Wan was devastated. He hid Anakin's infant children, Luke and Leia, and lived as a hermit for twenty years until he was killed helping the twins escape their now-evil father's clutches. Afterward, he took the form of a "Force ghost" and continued to teach and assist Luke.
Obi-Wan is a relatively stable character, with little angst or drama save where Anakin or Qui-Gon are concerned. He doesn't have any relevant romantic others (there was one in the EU, but she didn't work out) and he is very much devoted to the Jedi order. Hence, in prequel-trilogy-era fic, he's mostly seen when giving support to Anakin or as a foil to Anakin's harsh temper. Most fic concerning the classic trilogy occurs after his death, so his death is sometimes referred to as angst material for Luke Skywalker, and he sometimes appears as a ghost.
He also is sometimes paired with Asaji Ventress, a dark Jedi that he has confronted many times and has a lot of amusing banter with... or even with Padmé, verifying Anakin's suspicions about being a cuckold.