The Black Adder
Edmund (Rowan Atkinson) is the weedy second son of a macho medieval king (Brian Blessed). Tired of being forgotten about, he decides to dedicate himself to evil, taking on the soubriquet, "The Black Adder" (his first choice was "The Black Vegetable", but his cunning manservant Baldrick (Tony Robinson) advises him against it). Throughout the series, Baldrick comes up with a number of cunning plans to secure the throne for Edmund, but each of these is ballsed up by the idiotic Edmund and his dopish friend Percy (Tim McInerny). This series was written by Rowan Atkinson and Richard Curtis, "with additional dialogue by William Shakespeare".

Blackadder II
Edmund Blackadder (Atkinson again, of course) is a nobleman and favorite of the demented and homicidal Queen Elizabeth I (Miranda Richardson). His closest companions are his manservant Baldrick, who in this series is close to brain-dead ("For you Baldrick, the Renaissance was just something that happened to other people, wasn't it?"), and his foppish friend Percy. In this series, Blackadder is more convincingly evil, and is constantly occupied in various ruthless schemes to curry favour with the Queen, and to avoid having his head removed on one of her whims. The Queen's other sycophants include Lord Melchett (Stephen Fry), who is Blackadder's arch-enemy. This series features guest appearances by Rik Mayall as Captain Flasheart and Hugh Laurie as a vengeful German master of disguise. This was the first series written by Ben Elton and Richard Curtis (the team who wrote all subsequent series).

Blackadder the Third
Edmund Blackadder is a professional butler with ideas above his station, in the employ of George, the Prince Regent (Hugh Laurie), who is ostensibly ruling the country, because his father, George III, is as "mad as a balloon". The Prince is, in his own words, "as thick as a whale omelette", and is mostly interested in sleeping, eating and girls, when he can get them. Blackadder is assisted by Baldrick, who again is barely sentient, and has developed a great affection for turnips. Blackadder doesn't seem to have any particular game plan in this series, apart from striking it rich, either by rigging an election, publishing a novel or impersonating the Prince among other schemes. This series features guest appearances by Robbie Coltrane (as Samuel Johnson) and Stephen Fry (as the Duke of Wellington).

Blackadder Goes Forth
Despite his ancestor in the previous series ending up assuming the identity of the Prince, in this series Edmund Blackadder is a career soldier, a captain in the British Army. His peacful life of supressing colonial rebellion is shattered by the outbreak of World War I, and he finds himself installed in a trench near Flanders. The troops under his command include his batman Baldrick and Lieutenant George (Hugh Laurie), an inbred public school yahoo. Blackadder's objective in this series is very clear: avoid at all costs "going over the top" to certain death. To this end, he is engaged in a constant battle of wits with Captain Darling (Tim McInerny), staff officer to the insane General Melchett (Stephen Fry). His luck runs out in the final episode, when he and his troops can no longer avoid advancing on the enemy, and leave their trenches to certain slaughter. This series features guest appearances by Rik Mayall, reprising his Captain Flasheart role as a philandering flying ace, and Jeremy Hardy as a camp prison guard.

I will add Blackadder's Christmas Carol later.