Just to keep it simple these are the titles I remembering him having as of the close of A Dance with Dragons.
- Lord of Harrenhal (given to him by Joffrey after the Battle of Blackwater for facilitating the alliance with the Tyrells)
- Lord Protector of the Vale (gained by marrying and subsequently murdering Lysa Arryn)
- Lord Baelish of {insert name of the Fingers his land is on?} (gained by family inheritance)
Does Littlefinger hold any other titles?
Backstory: I am wondering because it appears his endgame may eventually be the Iron Throne...
Edit: Related: What is Petyr Baelish's endgame with Sansa?