I don't have much to add here but a brief explanation of each type, in case people need it.
Sarcasm:
"Oh, you are mowing your lawn, I see"
"No, I'm on the International Space Station doing some important experiments for NASA"
Satire:
Queen Elizabeth I was bald and had wooden teeth and yet somehow managed to remain a virgin.
Irony:
The fact that Alanis Morissette wrote a song called Ironic despite having no concept of irony. Finding spoons when you need a knife is not ironic. The weather on your wedding day is not ironic. Her writing this song is ironic.
Slapstick:
Moe pokes Curly in the eye with a finger.
Observational:
Why spend £500 on a tiny bag only big enough to carry lipstick? For £500 you could hire someone to walk behind you, carrying the lipstick.
Surreal:
Dolphin putting up some shelves underwater while the Baader-Meinhoff Gang dance past carrying huge hearing aids which blast out Billy Joel songs.
Punning:
I'm reading a book about anti-gravity. It's impossible to put down.
Schadenfreude:
Man slips on roller skates and falls downstairs.
Practical jokes:
Anything where there's a set-up to convince someone of something that isn't true for the sake of humour.
Situational:
A scene from Friends. Any scene will do.
Epigrammatic:
Quotation is a serviceable substitute for wit.
Lazy/rude:
Faggot!
Offensive:
Jokes about children who have been raped and murdered.
Sarcasm:
"Oh, you are mowing your lawn, I see"
"No, I'm on the International Space Station doing some important experiments for NASA"
Satire:
Queen Elizabeth I was bald and had wooden teeth and yet somehow managed to remain a virgin.
Irony:
The fact that Alanis Morissette wrote a song called Ironic despite having no concept of irony. Finding spoons when you need a knife is not ironic. The weather on your wedding day is not ironic. Her writing this song is ironic.
Slapstick:
Moe pokes Curly in the eye with a finger.
Observational:
Why spend £500 on a tiny bag only big enough to carry lipstick? For £500 you could hire someone to walk behind you, carrying the lipstick.
Surreal:
Dolphin putting up some shelves underwater while the Baader-Meinhoff Gang dance past carrying huge hearing aids which blast out Billy Joel songs.
Punning:
I'm reading a book about anti-gravity. It's impossible to put down.
Schadenfreude:
Man slips on roller skates and falls downstairs.
Practical jokes:
Anything where there's a set-up to convince someone of something that isn't true for the sake of humour.
Situational:
A scene from Friends. Any scene will do.
Epigrammatic:
Quotation is a serviceable substitute for wit.
Lazy/rude:
Faggot!
Offensive:
Jokes about children who have been raped and murdered.

About all I do with my life outside of work is go to see live comedy, either stand up, musical or theatre. I like to see a range of acts. Keeps shit interesting.
Some great Aussie comics come to the northern hemisphere too now. The sense of humour doesn't seem any different at all; just the cultural reference points. And we get enough Aussie TV that we understand most of the Aussie reference points anyway.
I moved to Melbourne partially to be able to go to the Comedy Festival without the restriction of only having a week. Out of 300 acts, I often go to about a 50ish. It makes my brain bleed but I love it.
I would LOVE to go to the Edinburgh Fringe one day. But I suspect it would kill me.
I've done the Fringe a few times (I'd go every year if I could get the time off work). I guess you'd expect me to say it's not quite what you imagine or it's not as good, or burst your bubble in some way, but it's just the best thing in the world. It's a beautiful city anyway, but when it's buzzing with comedy and all the stuff that goes on in the street? If you ever do make it, though, one tip for you: don't stay in the city. Stay somewhere well away like Stonehaven and travel in each day. Apart from keeping your sanity, Stonehaven is a beautiful, peaceful base.
Oh, and a second tip. When people press you to attend what sounds like the maddest thing ever, you should go. Sometimes it really is just weird (like the show about a woman assassinating the character of her hairdresser), but sometimes you hit on something just amazing and you and the fifty people in a crappy room have an experience you'll never forget. :)
I wouldn't even know how to define my sense of humour, I laugh at all sorts. I'm very fond of sarcasm, satire and irony though, being English and all.
From your list, punning wins, that pun cracked me up! I'm a sucker for a good pun!
Tim Vine!
P.S. But then, you probably already knew. :P
My friend always wanted to be run over by a steam train. When it happened, he was chuffed to bits. :D
"But I'll tell you what I love doing more than anything: trying to pack myself in a small suitcase. I can hardly contain myself."
"So I got home, and the phone was ringing. I picked it up, and said 'Who's speaking please?' And a voice said 'You are."
Pahahaha, I think I'm in love! I think I might actually die of laughter. In fact he might just have a chance of replacing Sean Lock as my favourite comedian:O! Thank you very much, you've just made this banana very, very happy:D!
A couple of my favourites:
A friend dropped his scrabble set in the road. I said, "What's the word on the street?"
Crime in multi-storey car parks. That's wrong on so many levels.
I've seen him live. I was gasping for breath at one point because he delivers them so quickly. It's bang, bang, bang, and you never get to recover. Saw Sean Lock live too. He's a real favourite of mine. He just gets funnier and funnier year on year. I love Sean Lock. :D
P.S. Do you ever get that when you're half way through eating a horse and you think to yourself, 'I'm not as hungry as I thought I was'.
P.P.S. Milton Jones and Stewart Francis do a similar kind of comedy (both funny men and worth looking at) but Tim Vine is the absolute master of the pun.
I find observational, satire, sarcasm, irony, puntasticness... I don't especially like humour if the only joke is that it's offensive. If it's a good joke I'll still laugh, but the shock factor alone isn't enough.
My favourite comedian is probably either David Mitchell or Dara O'Briain, but it changes from day to day. There are too many that I love to name :P For me puns don't always work in a stand-up setting, but I adore Milton Jones for puns; he's brilliant.
I've hardly even looked into American comedians either... there's just so much good comedy in the world! :) I really like Bill Hicks, but I've not seen much of him yet.
Also, you should have added musical comedy. I swear Tim Minchin is one of the funniest men alive, and his songs are pure genius. My favourites are "Taboo" and "Storm". Everyone should YouTube those.
You like exactly the same people I do. I've worked out David Mitchell's schtick but I still really love it. Dara is someone I'll love until my grave because he's actually a really nice man considering his profession.
As for Bill Hicks, I think he's the funniest American who ever lived. Apologies to Lenny Bruce, and Richard Pryor.
P.S. Tim Minchin's Angry (Feet) is still one of the funniest things I've ever seen.
IIN is a great source of comedy as well :)
But what I will do is to recommend live comedy to you almost as a religion. When you are part of an audience that's being worked by a comedian who knows what he is doing, something inside you soars.