I'd be writing all day if I mentioned every series I really, really liked, so I'll just mention my Star Picks!
The Vorkosigan Saga, by Louis Macmaster Bujold - starts with his mother meeting his father, then goes through his life from childhood upwards.Takes a little getting into, but once you read a few, you get to know all the characters, and get all the 'in-jokes' between them. Series is still being written, but each book can be read by itself if you don't get annoyed by occassional references to things from other books.
The Seafort Saga, by David Feintuch - another generational series, from the main character's youth, onwards to his son as well. An epic series of naval tradition, military action and intrigue among the stars!
And finally, a series that influenced science fiction culture, and began before shows like Star Wars, and before roleplaying games like Traveller existed:
The Dumarest Saga, by E.C.Tubb - these are small paperbacks, and I think the series is around 30 books long. Follows the life of a man who was born on 'earth', a world that most people don't believe ever existed. He travelled deeper and deeper into the galaxy, exploring, adventuring, experiencing space life, and then had a desire to return to his home - but no one knows where earth is, and it's not on the star charts or anything. There's also secret cults, galactic conspiracies, and all the staple 'classic' sci-fi scenes, such as gladatorial fights to the death, cybermen, space princesses, telepaths, and more! These are my favourite books of all time, even though they're so small!
