yeah yeah yeah
Humphrey Bogart, with the trenchcoat and hat, smoking a cigar. Actually, rakish to me refers specifically the tilt of his hat.
Since my example is so different than everyone else’s I thought I’d explain: the first time I ever hear the word “rake” (oh so many years ago) was in reference to Ben Franklin – since it turns out he had a bit of a naughty streak. From then on, I’ve always associated the word with uncular, racy old men. Not in a bad way, you understand (hence Burgess Meredith in “Grumpy Old Men”).
Oh, and only certain hats can be worn at a rakish angle. Fedoras, definitely. If you’re wearing your fedora at a non-rakish angle you’re just square. Bowlers/derbies, perhaps, if you’re an Avenger or a villain.
This word, of course, should be avuncular.

SUCK-UP!
I initially think of the hat angle, and then sexily naughty, like that old song “Somebody’s knockin, should I let em in…it’s the Devil…I never dreamed…he’d have blue eyes and blue jeans.”
An azure-eyed, denim-clad demon would be “rakish”.
Suck-up I may be, Sidle, but I know all four gentlemen intimately and I can assure you that they are not only rakish, but are well worth sucking up to.
I also think of the rakish tilt to a fedora. And the attitude that goes with it. Suave, smooth, but not in a dangerous way. A handsome, debonair, stylish man who does not look for trouble, but if trouble finds him, he can deal with it.
A ladies man, definitely, but not a cad. He’s got an easy way with women about him, but he is, above all, a gentleman.
In short, a guy like me. 
Just out of curiousity, Sophie, why do you ask?
I must go watch Errol Flynn movies now…sigh…
I’ll take myself out of the running and offer **Lord Byron **.
As someone who was involved in the original, somewhat more private discussion of the word and its place the vernacular, I’d like to pose a side question…
How many of you think the words “rake” and “rakish” imply some degree of promiscuity?
Doesn’t rakish mean in the style of a rake ala rake-like?
Yes. Just like “fish” means in the style of an “f”.
The word “rakish” implies some degree of promiscuity, but nearly so much as “cad.” A rake is someone who might have success with women, but sincerely like them, whereas a cad is a love 'em and leave 'em type. “Rakish” implies even less promiscuity to me, since, as delphica wrote, they’re not necessarily a rake, they just act like one. One can be rakish and still be a gentleman. A cad forfeits all claims to gentlemanliness.
Wow, uh…how you doin!
Damn. I read the thread title and immediately thought, “Mad, bad, and dangerous to know.” But cuate beat me to it.
I’ve also heard it used to describe cars, usually with fins, fancy grills or chrome exhausts.
Nowadays, I hear Montgomery Burns using the word to describe something.
Rakish.
Sounds like some Middle-Eastern opiate-laced clove cigarette.
Actually, I think it just means gaudy beyond good taste.
Rakkish is CLEARLY to be of a Rakk-like nature.
DUH. 
Wow. I think that this definition amuses me more than any of the others.
Oh, this gets me, right where the gettin’ is good.