Egypt for me too. I had such a fantastic time there!
Two full page visas for me, one for Belarus and one for Russia. 
What was funny was because there are no passport checks at the border with Belarus and Russia, I’ve got an entry stamp for Belarus, but only an exit stamp for Russia! :rolleyes:
Two holes from the staple that held a page I had to tear out.
Otherwise, probably USSR.
My passport was almost full, only one clear page left. But some countries put a full-page sticker in and I had a few of those. The next destination was overland, on road and at night, and the sticker came off pretty easily. So, on the plane, I de-stickered a Chinese visa, which left a faint marking but the overland border either didn’t see it or didn’t care.
That was quite a buzz.
In my current passport: the visas for Kenya and Israel.
A few passports ago: my 10 year, multiple-entry US visa. The standard at that time seemed to be a 5 year visa, but for some reason the staff member at the US consulate gave me a 10 year one. It drew comments of wonder and awe from customs officers all over the world…“a 10 year US visa? How on earth did you manage that?”
The irony was that I used it only once.
Probably the one from the Seychelles… Google it to see what it looks like. 
Since I posted in this thread, I’ve been to Nagorno-Karabakh. I don’t think they get much cooler than that
I’ve gone through many passports in my life, but I always liked the stamps that did not use the Latin alphabet: Greece, with the Greek alphabet, of course; and Morocco, the stamp of which was in Arabic and French.
I have a visa in an old passport for Afghanistan from 2002 issued right after the Taliban had fallen. It’s just a hand typed piece of paper that someone cut out, pasted in to my passport and that the ambassador had signed. I also have a stamp from “Kurdistan” that the Kurds in northern Iraq put in my passport, but whic the Iraqi authorities didn’t recognize as an entrance stamp, so I was in the country illegally.
The US visa in my passport is quite interesting and colourful.
Before the advent of stickers, Nepal had a lovely, full page, multi coloured stamp, entry visa that was a thing of beauty. Still the nicest one I’ve ever gotten, though it’s in an old passport now!
Second place would be Bolivia, a stamp like a postage stamp - not a rubber stamp. And quite lovely.
But now I’m a little confused: coolest, as in from the coolest place? Or, coolest, as in coolest looking?
Czech, by default, although it’s pretty dull.
A friend of mine sat next to R. Crumb on a flight once. In lieu of an autograph, he took out a rubber stamp with (I think) Mr. Natural and nailed a passport page. I envy that more than your multicolor Nepal whatzis.
My coolest are the Entry by Sea stamps from the Caribbean. I know all the cruise ship passengers have the same stamp, but I traveled by private sailboat. When we arrived in the new country we would anchor in the harbor and hoist the Quarantine flag while the yacht’s captain (my husband) took the passports of all the crew and take the dinghy to the police department/customs house to check us all in. Meanwhile the rest of us all had to stay on the boat (drinking rum punches).
Great memories.
By default, China. Full page visa sticker with the Great Wall on it.
Our daughter actually has a Chinese passport, which is neat, although no longer usable, since she’s no longer a citizen.
Coolest one may be Nepal. Prettiest one is possibly China, the full-page Great Wall sticker mentioned elsewhere in this thread. But Laos, Vietnam and Cambodia have pretty full-page visas too.
The 10-year US visa in the wife’s Thai passport is quite colorful too.
Oh, and if we’re talking current passport, I had mine renewed not too long ago, and it just has some dull stamps for Thailand, Japan and Singapore in it now.
EDIT: Actually, thinking about it the coolest one may be from East Germany or Czechoslovakia, both of which don’t exist today. Got them back in the 1980s along with Nicaragua.
My first passport was so full of stamps that I had to get extension pages.
Singapore, Malaysia, Indonesia, Australia. Indonesia always took a full page and I was going in and out on a regular basis.
My second had one stamp only - S. Korea.
I used to travel out of Thailand much more than I do now.One of my passports had to have so many extra pages added that it began to look like a phone book!
Back in the day, extra pages were free. You just walked into the nearest US Embassy, said “Extra pages, please,” and then you were merrily on your way. But now they charge a fee of $82 for them, which is not far off the price of a new passport.
I had to get extra pages in my last US passport. Since I’ve renewed that passport, though, I’ve also picked up an Irish one, which means I no longer get stamps when travelling within the EU. I tend to use my US passport to enter the US and my Irish passport to go everywhere else, but so far the only non-EU/non-US place I’ve been with the Irish passport is South Korea, so that’s the only stamp I have in that one.