This is neither here nor there, but...
A few months ago, I ended up running a D&D game at a friend's house with absolutely nothing but a PHB, the online SRD, and a handful of Yahtzee dice. It's a long story; we were all hanging out, got bored, someone suggested we play. So I hammered out a quick dungeon crawl while they scribbled up some character sheets on notebook paper, and rolled up some fourth-level characters. But when it came time to play, we realized that we only had six-siders for dice.
I was loving the spontaneity of the situation, and I didn't want to kill the spark by drowning it in math. So to keep the flow, I quickly ruled that 3d6 would be used instead of d20s, and off we went. Other rules were improvised as needed...d4s were replaced with d3s, d% were replaced with red and black poker cards, and so forth.
Turns out, replacing d20s with 3d6s didn't break the game. At all. In fact, it had the opposite effect...it gave the game a much more balanced feel. Without critical hits, automatic success/fail, or the upper and lower extremes of the d20 scale, combat was a lot less "swingy," attack rolls were a lot more reliable, save throws were a lot less sensitive, and that's pretty much all. Dice mechanics aside, the characters were still adventurers, exploring the haunted ruins of Castle Wherever. It was a blast.
I'm not saying that I am ready to ditch my d20. I too have an unnatural affection for that polyhedric ball of triangles, and I will use it at every opportunity. But that Saturday afternoon of improv gaming really changed my perspective on the 'd20 vs. 3d6' debate. It was one of the most entertaining games I have ever played, hands-down.
I concede that not everyone would have enjoyed it. Some folks really like the symmetry of balanced math, where one has an equal chance of rolling a 3 as they do a 12, and that's cool. And not everyone likes to deviate from the rules-as-written either, for any reason, and that's cool too. I'm not trying to change the way anyone plays the game.
But don't sweat it if you accidentally leave your dice at home. It ain't no thang.