Batman's nemesis, The Joker, behaves in exactly the same way as the playing card that inspired him: he's a mysterious figure who spreads random havoc by his very appearance. The character has been reimagined many times (seventy years of multi-media continuity being what it is, it's difficult to call it an 'evolution'), but those basics have remained: the grinning lunatic of mysterious providence who causes mayhem for little more than its own sake.
The Joker was originally a pyschopath who would poison victims with a strange toxin that left them dead with a hideous smile on their faces. In the post-Wertham 50s and 60s, he became little more than an annoying a clown whose modus operandi was to set up some kind of ridiculous robbery caper, laugh, get beaten up by Batman and delivered to the police. Locked up in Arkham Asylum, he would then escape and then we're back to square one. Cesar Romero's ultra-camp performance as the Joker in the 1960s BATMAN TV show was difficult to take as any kind of serious threat.
In the hands of a succession of writers, the Joker slowly had his teeth restored, starting with Denny O'Neil and culminating most famously in the Alan Moore/Brian Bolland story THE KILLING JOKE, in which the Joker cripples Barbara Gordon, daughter of the Commissioner and alter-ego of Batgirl; effectively restoring his status as a serious threat in Batman continuity. But even with this auspicious team behind him, the Joker was little changed from his original days. Jack Nicholson's version of the Joker in the 1980s Tim Burton movie is much more in line with this restored vision of the Joker, although he's as much Crazy Old Jack as he is the comicbook icon.
A number of postulated origin stories have been postulated for the Joker; most of which see him disfigured by falling into a vat of chemicals with the unlikely result of dyeing his hair green and his skin white). Many of these origins also show him running around as proto-supervillain "the Red Hood" prior to this accident. None of these different origins have stuck: I think that do pin a definitive origin onto the character would destroy his appeal. The power of the Joker is that you don't know from whence it came... but once it appears, all bets are off.
I believe that the most definite change in the character since the 50s came in the recent screen: the late Heath Ledger's portrayal in Christopher Nolan's 2008 film, THE DARK KNIGHT. This (deeply flawed) film has quickly become one of the most popular of Hollywood's comicbook adaptations, and I believe that this is entirely due to their handling of the Joker.
The Ledger/Nolan Joker raises the stakes in several ways. Ont he surface, they've substituted the chemical-bleached skin and hair for makeup. Smudged, smeared makeup, which fails to conceal the mutilated face beneath. Even the Joker's lips are scarred, and his speech is effected by the way he keeps licking them. This Joker is not a scary clown, he's a disfigured freak, and there is nothing remotely funny about his appearance. His jokes are not funny, either--he admits it with some pride. His jokes are not funny at all. Gone is the prancing, flamboyant Joker we've long since grown accustomed to. Gone the false English accent, the ridiculous props, then novelty weapons. The Ledger/Nolan is frightening and capable. This Joker won't surprise you with an exploding cigar... he will stab you to death with a ballpoint pen.
Ledger's Joker has no desire for material gain, all he wants to do is to spread chaos and madness for no better reason than because he can. He comes with his own conflicting set of origin stories, each of them nastier and more real than any of those postulated in the funnybooks--because this Joker has invented them himself.
