Vimes (and half the other characters present) at the climax — he arrests two entire armies (including his own side) as they stand on the battlefield, charging them with breach of the peace, loitering with intent, loitering within tent, malicious lingering... and carrying a concealed weapon, simply because he doesn't happen to be looking at the weapons at the time. He also arrests the leader of the opposing army for murder and threatens to shoot the leader of Ankh-Morpork's army. At which point Captain Carrot organises a football game.
Then there's this line, in regards to Carrot having talked the D'regs into not charging.
"This man can make water run uphill and he has a commander."
For fans, it's difficult to decide whether that statement is a more awesome testimonial for Carrot or for Vimes.
Vetinari usually gets these near the ends of most of the stories he appears in, after orchestrating elaborate plans and Roulettes that work out to improve Ankh-Morpork for the better. Vetinari is badass.
The knife-juggling stunt, which consisted of Vetinari juggling three melons and three knives at the same time (it is pointed out that this is harder than six of either item, because of the differences in shape and weight). He then goes on to use the knives to cut the melons in half in midair. Furthermore, on the next page, he claims that "Until now, I've never tried it."
That is, he's never tried juggling. Of any kind.
Apparently it's a cake walk compared to running Ankh-Morpork.
His excuse: "One knows where the objects in question are, and where one wants them to be. What more does one need?"
Vetinari surrenders the island of Leshp unconditionally to the Klatchians, leading Lord Rust to charge him with treason. Knowing that the island will sink back under the sea in a few days, he arranges for the treaty-signing to take place there. Thus, the treaty becomes null and void, the Klatchian leader is disgraced, and, since he didn't sign a treaty to surrender a nonexistent island, all charges against Vetinari are dropped.
Vetinari: All I know, my lord, is that Prince Cadram has, at a politically dangerous time for him, given up a huge military advantage in exchange for an island which appears to have sunk under the sea. The Klatchians are a proud people. I wonder what they will think?
And Vimes' response when the city leaders reluctantly tell him that he has to let Vetinari go. "Well, if you think of anything to charge him with later, just let me know and I'll go arrest him again. I know where he lives."
"VENI. VICI. VETINARI." -you don't need other words.
71 Hour Ahmed. Basically the closest thing Discworld has to a Cowboy Cop and about equal to Vimes on nearly all counts, but especially when he points out to Vimes that both of them suspected their own countries on principle when the other country was incriminated, and the only difference was that Ahmed happened to be right.
In the same scene when Vimes reasons out that Ahmed is actually also a watchman.
Prince Cadram: Well, Mr Samuel, when I raise my hand, the men behind me will cut you d-
71-Hour Ahmed: I will cut down the first man that moves.
Prince Cadram: Then the second man that moves will kill you, traitor!
Captain Carrot: (Drawing sword) They'll have to move very fast.
A possible, though creepy, case of Fridge Badassery for Vimes: In the alternate timeline where Klatch invades Ankh-Morpork, after Detritus (badass troll), Dorfl (badass golem) and Carrot (badass incarnate) die, Vimes is still the last man to be taken down.
Props to dimwitted, stupid Colon for accurately guessing Prince Cadram's plan simply by being Too Dumb to Fool and not being politically correct like his boss.