I thought all 4 Blackadder series were good, but the first wasn't quite as good as the later three. I think it had a lower budget and different writers/producer from the later three series (I forget the details).

I liked the way they sang words to the closing theme tune in the 2nd series, to reflect the episode contents. Here's the one from my favourite episode mentioned above, entitled "Beer":

Blackadder couldn't hold his beer,
The art of boozing he's not mastered.
And I, your merry balladeer,
am also well and truly plastered.

Blackadder, Blackadder,
A bit like Robin Hood.
Blackadder, Blackadder,
But nothing like as good.

Blackadder, Blackadder,
I thought that he had died,
Blackadder, Blackadder,
The writers must have lied

or this one, from "Potato" (where Blackadder goes to sea in the footsteps of Drake and Raleigh):

Sir Francis and Sir Walter had
Discovered New Worlds and new nations.
And though Blackadder thought them mad,
He tried his hand at navigation.

Blackadder, Blackadder,
He saw the oceans foam.
Blackadder, Blackadder,
He should have stayed at home.

Blackadder, Blackadder,
He heard the New World call.
Blackadder, Blackadder,
Discovered bugger all!