I will also suggest
Runaway Series, which I loved the most. You should also definitely try all three seasons of
Sam & Max.
Now as everybody said there aren't much sequels around. Games get mostly only two sequels. But you should definetly check out
Agatha Christie games and all the other Adventure Company games. Also look into
Sherlock Holmes game series (there are 6 games)
You might also want to check out Post Mortem, Still Life and Still Life 2 which are all connected. Also definitely check out Syberia and Syberia 2. All these games are done by
Microids