What are the things that happen in most/all of the series?

Blackadder is imprisoned.
He encounters a girl dressed as a boy.
He encounters Lord Flasheart twice, three times if Mad Gerald is a Flasheart.
There are multiple deaths in the final episode.

Anything else?

Well, for the first three seasons, he was really close to the monarch of the time (he even was the king's son in the first season).

He always ends up with stupid people as he closest friends/companions. Percy, Baldrick,the Prince Regent, Lt. George, Cpt. Darling, not to mention at least two different generations of Melchit's!!