Grand Master Yoda was the leader of the Jedi Council in the first three Star Wars movies, and in the last two he trained one last student in the ways of the Jedi. Yoda was a master of acrobatic lightsabre combat as well as being powerful enough to dispel Force Lightning with his bare hands. Previously, Yoda's species was unknown, but recent developments in the Star Wars mythology hint that Yoda is theoretically a Gree (an extinct species of alien).
Yoda the Master
Yoda was the oldest Jedi Master on the Council and indeed was often seen as the very personification of the Jedi Order. Despite his wizened and worn character, Yoda remained shockingly spry for a creature of his advanced years, and he was more than able to turn backflips and somersaults in his battles against his renegade former padawan, Count Dooku.
Yoda was one of several Jedi masters who never fully accepted Anakin Skywalker into the Jedi Order. Although he allowed both the boy's acceptance and his promotion to Jedi Knight, Yoda always felt that Anakin would have a disruptive effect on the Jedi.
Yoda the Hermit
Following the events of Revenge of the Sith, Yoda hid himself away on the distant planet of Dagobah. Here he would live out the last 22 or so years of his life, and in his twilight years train Luke Skywalker in the Jedi arts. However, Yoda never seemed confident of Luke's ability to overcome his father's legacy.
Skills and Abilities
Master Yoda was probably the most powerful Jedi of his day, though he was arguably rivaled by Mace Windu and would surely have been surpassed by Anakin if not for his fall to the Dark Side and subsequent crippling injuries on Mustafar. Yoda fought the Sith Lord Count Dooku to a standstill, and even survived a duel with Darth Sidious. During both of these confrontations, Yoda demonstrated powerful telekinetic abilities with the Force, including stopping the fall of a massive column during his duel with Dooku and stopping a senate pod hurled at him by Sidious, which he then sent hurtling back at the Sith. He was the only Jedi known to be able to repel Force lightning without a lightsabre.
Yoda was also a master with the lightsabre, using a form which emphasised agility to overcome his small size and advanced age. Additionally, he was unusual among Jedi of the Clone Wars era in that he demonstrated some tactical skill at commanding a large scale battle.
Renowned for his wisdom, Yoda nonetheless clung to the ways of the old Jedi, which helped alienate Anakin Skywalker and contributed to his fall to the Dark Side. According to the Revenge of the Sith novelization, Yoda realized during his duel with Sidious that he could not win, due to the Jedi's failure to adapt under his leadership. This epiphany may have influenced him in his decision to allow Luke and Leia to be raised with families, contrary to the traditional Jedi view which emphasized a lack of personal attachments.