This improv system works for systems with ascending AC--where the foe's AC is your target number on a d20...
Like Penny, Nickel, Dime, Quarter, Dollar it isn't perfect, but it has stood me in good stead through many random encounters and is a useful thing to have around as a last resort if you do a lot of improvisation when DMing.
So you got all of a sudden a monster but--d'oh--no stats because it was just unexpectedly summoned or invented.
So this: roll d20 to hit, but when you roll that, also roll another die: if it's like a relatively wimpy monster like a goblin chief roll a d4, if it's like Beelzebub or what-all, roll a(nother) d20, and if it's something in between, roll a die whose value's in-between. Like if it's a troll roll d12.
Add the 2 dice together--that's the monster's total to-hit roll this round. Nothing to write down--if it's, for example, a d8 monster (say, a gargoyle) you just roll a d8 with that d20 every time. Its "bonus" will vary every round.
Basically, if you're scaling the adventure to the PCs, choose the die where the high end matches or slightly exceeds the toughest player's bonus, and if it's a boss go two or more dice up. If you're not scaling just use the die equal to twice where you'd put the monster on a toughness scale from 1-10.
The scale's easy to remember because you stare at it the whole time you're DMing: d4, d6, d8, d10, d12, d20.
And if you wanna be super lazy, you can use that second die as its damage roll, too.
This all ignores a lot of detail that separates one monster from another, but if you need a "hideous mutant from the bottom of the spawning chamber" out of nowhere all of a sudden, you can do worse than (say) 8 hd/d20+d8 to hit/d8 damage and sort the rest out if and when it comes up.
If it was fighting 3.5-style PCs I'd give it 2 attacks or a +8 bonus to damage, too.
Wars of Exilon
1 hour ago