I had a random thought : Does Petyr Baelish still have any relatives? What happened to his parents? Any siblings? Any children, legitimate or illegitimate?
The device painted on the shield was one Sansa did not know; a grey stone head with fiery eyes, upon a light green field. "My grandfather's shield," Petyr explained when he saw her gazing at it. "His own father was born in Braavos and came to the Vale as a sellsword in the hire of Lord Corbray, so my grandfather took the head of the Titan as his sigil when he was knighted."
(A Storm of Swords: Blood and Gold, p.357)
So Littlefinger's great-grandfather was Braavosi, but his grandfather was a Westerosi hedge knight.
And on the next page:
"Well, you can scarcely be my true-born daughter. I've never taken a wife, that's well known. What should you be called?"
"I ... I could call myself after my mother ..."
"Catelyn? A bit too obvious ... but after my mother, that would serve. Alayne. Do you like it?"
So his mother was named Alayne, and he has no legitimate children. As for illegitimate children, there is speculation that Robert/Robin Arryn may really be Littlefinger's bastard son and even that Sansa Stark may really be his bastard daughter, but no confirmation either way.
Quoting from an interview with GRRM:
In response to the why was LF fostered at Riverrun when he was a insignificant lord question: GRRM said that Petyr's father and Hoster met up during the War of the Ninepenny Kings and became friends. Apparently that was a time when a lot of people from all over the realm forged friendships. LF's dad later "cashed in" on the friendship to get LF fostered at Riverrun.
So his father was sufficiently high in society to be considered a friend by Lord Tully.