I have been to dinner with people who will say “a votre sante” and then the men will add “et a votre beaute” in honor of each woman at the table.
In his autobiography Boy, Roald Dahl describes the whole “skaal” ritual.
I am trying to remember what my family uses, when we do use it. It’s so seldom. I think it’s just “cheers.”
Gan Bei!
Chinese for “dry cup”, which is what they say.
A favourite of mine is “Over the river, men!”
Yeah, this is a popular one in my circles as well.
Often answered by the goup with “No babies!”
And occasionally someone else chimes in with: (Uh, it’s a little indelicate)“Blood in yer undies!”
I’ve recently succeeded in getting my parents to say it. 
“Cheers, m’dears!”
“Here’s to us!”
“Here’s to good food, good times, and good friends.”
I’m reminded of the creepy scene in Hedda Gabler when the scoundrel says what I now know as “Skaal, Thea, skaal”…we listened to this repeatedly on vinyl as kids and I had no idea what he was saying, just that it sounded really sinister!
Upon googling, it’s Eilert Luvborg…shudder
An Irish favourite of mine:
“May you be in heaven half an hour before the devil knows you’re dead.”
I also like “yum boi” (Cantonese for “gam bei” as noted above), another vote for “sláinte” (pron. “slon-shu”) because my missus is an Irish speaker, or “iechyd da” (pron. “yack-id-a”) because I know a lot of Welshies.
But the one I use most is “chin chin”, because it’s a gently mocking homage to the era of Noel Coward and all that wonderful 1920s stuff. I believe it’s Italian.
I never use “Cheers.” More often it’s “skol” or “prosit.” On a television story about South African wine, the vintner said his usual toast is “Gesundheit,” meaning “to your health.” I have a few longer ones, if I feel like it.
“May the wind at your back not be your own.”
“Let us drink to what we all drink to, eventually. To drunkenness.”
“Here’s to all the kisses I’ve snatched, and vice versa.”
Most of the time, I drink to my lovely, brilliant wife.
Mmm. I like that one.
Someone mentioned the raised glass vs. clinked glass connundrum, so I had to mention this: I went out for drinks with birdsister in Spain & we ended up knocking glasses with a few locals. When doing so, I looked them each in the eye & they got very pleased. In broken English, I was told this: “We believe you should look in the eyes. If not, it is seven years bad sex.” I doubt this is an all-over Spain thing, but I started noticing who does it and who doesn’t. Americans usually look at the cup, while the British folks I know seem pretty split. The only German people I’ve met since stared a whole in my head.
Drinking with a group of Vietnamese men, you’ll likely confront a weird, macho version:
The host will pick another member of the table, and the two men will decide on an amount they have to knock back in one go, expressed as a percentage. Usually, this is 100% Then he’ll say “DRINK!” and the host and the guest will both knock their drink back in a sort of race, then try to be the first to show the empty glass to the others, and also try not to cough or splutter (a bit hard with some of the local rice spirit).
Over a few drinks, each person should be ‘it’ at least once. In practice, the 6’4" white boy at a table of farm hands out in Bhut Phuc village will be ‘it’ most of the time, especially when, unknown to him, his cheeky Vietnamese friend arrived in the country two weeks earlier and threw down an unwanted challenge on my behalf, ‘wait until my Western friend arrives. He’ll drink you all under the table.’ Bastard. 
A hole Goddammit!
Being Scottish on my dad’s side and German on my mother’s, I usually go with sláinte mhath (pronounced “slaun’cha va”) or prost, but cheers is always appropriate.
For some other ideas, take a look at this site, which gives you “cheers” in 50 languages.
Skål.
I’ve always liked “Here’s to space”
And when people invariably ask me what I mean, I tell them the little rhyme:
I always say, “Here’s to it.” I think it’s a short version of a toast a freind’s dad used to say:
Here’s to it, and from it
And to it again
If you don’t do it when you get to it
You may never get to it again.
He also used to say:
*Here’s to heat.
Not the kind that ignites and brings down shanties.
But the kind that excites and brings down panties.
*
He had a million of 'em.
This is my standard toast:
“Here’s to good friends, tonight is kinda special.”
(I don’t drink Lowenbrau - I just bit their commercial)
Apart from the traditional “Skál!” (sounds like “scowl”), I tend to use the polish “Na zdrowie” or anything in German, such as “Auf der häßliche Zwerg!” (to the ugly dwarf) but usually less tasteful than that, when I get properly wasted (a “to the ball-point pen up my ass” caused me some trouble with German tourists last year). I don’t think I’ve ever said “cheers” when drinking–I only ever hear it as a british “thanks”.
Regretably, I picked up my typical toast from a movie, but I usually drink “to crime” when given the chance.
Na zdrave is the Bulgarian version. (To health.) Whilst looking the cheer-ee in the eye, of course.
I seem to recall drinking in Spain with some Norwegians that there was stomping of feet involved. But it’s a little hazy and I’m not sure if we were all mimicking the locals (Spaniards) or each other. That’s the best kind of dedication.
We tend to say ‘uff da!’, which is just a general grunt of happy meaning in most Scandinavian languages.
A Russian friend used to toast us with “Za vashuh zdroviyeh.” It meant “to your health.”
In English, my friends have commonly said, “To Us, because no-one else is likely to,” or “Here’s to our wives and sweethearts–may they never meet!”
Somewhat more poignantly, we have toasted “To absent friends,” when one of our number, who would normally be there, has died.
And then there a good friend of mine. No matter the situation or the company, he will raise his glass and say, “Here’s to the girl who lives on the hill. She won’t, but her sister will.”