Intelligent or not, Baldrick is always one for inventing "cunning plans", which are generally ridiculed by Blackadder, who nevertheless ends up using them. So much is the character associated with the phrase, "I have a cunning plan," that for example there is a landmine detection device that is so cunning that it is has been dubbed the Baldrick. (I heard about this on the radio in someplace like Cambodia or Afghanistan -- does anyone have a particular reference to it?)
Other traits shared by all Baldricks (except possibly the first one) are sheer disgustingness and an obsession with turnips.
Baldrick isn't given any sort of first name until the third series, when he speculates that it might be "Sod Off", since his childhood friends would say "Sod Off Baldrick". A diplomatic Blackadder opts to record him as "S. Baldrick" and come the next series, the credits read: Private S. Baldrick.
In the Blackadder pilot episode Baldrick was played by Philip Fox.
An indication of their relationship, from Blackadder II:
...See also: BaldricKATE The word is that your servant is the worst servant in London.
BLACKADDER Mmmmm. That's true. Baldrick, you're fired. Be out of the house in ten minutes.
...
BLACKADDER Sorry, Baldrick. Any reason you're still here?
BALDRICK I've got nowhere to go, my lord.
BLACKADDER Oh, surely you'll be allowed to starve to death in one of the royal parks?
BALDRICK I've been in your service since I was two and a half, my lord.
BLACKADDER Well, that must be why I'm so utterly sick of the sight of you.
...