Voted d6 (for simplicity and ubiquity--nobody, in or out of D&D, is gonna look at it and think "dice COME in that size???"--as well as being a platonic solid) and d20 (for having the biggest range, also being a platonic solid, and being D&D's iconic die). Unlike Lowkey, I see nothing wrong with being common--I see that as being a huge selling point, actually. From there, functional concerns primarily rule.
So my personal ranking (top down) would be:
1. d6 -- simple, universal, and the only die to have 90-degree angles. There's a good reason it's so universal.
2. d20 -- the iconic D&D die, and good for being meaningfully "big" compared to the d6.
3. d10 -- Half a d20, and perfect for simulating decimal-sized dice (percentile, permille, etc.) A versatile workhorse.
4. d12 -- It's also a Platonic solid, but when it's so easily covered by 2d6 and is only the teeniest bit better than 1d10, it's hard to justify.
5. d8 -- Really this could almost be ranked equally with d12: platonic solid (octahedron), only the teeniest bit better than d6, but harder to simulate than d12.
6. d2 -- Yeah, I went there. Flipping a coin is great--and half the time, it's more than enough randomness.
7. d4 -- Personally, I don't find them that hard to read, I just feel like they're in a no-man's-land, neither small enough nor big enough to be interesting.
8. d100 -- Pointless. A waste of a die. You get *precisely* the same result from rolling a d10 for each place-value--it's not even "simulating," it's mathematically identical.