d10s are the only dice that are worth having and using, all the other dice suck. d6s are baby toys, and who the fuck would in their right mind even use a d20? You could just as well roll a marble. d8s look like d6s that got the number of faces and vertices wrong and what the fuck is even a d4? What, you couldn't even afford a face that would, uh, face upwards? You have to read the value off of a point? At least d12s look cool, what with being made of pentagons and all. They're almost as good as d10s, but only almost.
Okay, now that I got the silly out of my system, let me get a bit more serious on this subject. I do believe that ten-sided dice are the best choice for tabletop RPG, a belief I share with Jacob, who nicknamed it rather beautifully "the glorious ten-sided master race". I don't know his reasoning, but my train of thought stems from what I think an ideal RPG should be like.
My ideal RPG would be focused on the role-playing aspect of the game, not on the sheet of paper that defines your character. It would be less about rolling high numbers and more aboput making the right choices in difficult situations. It should also not limit what kind of stories you can tell in them, by which I mean it shouldn't define special rules and, especially, rolls, because once it does, it starts to limit potential stories to a particular genre, or worse yet, setting. Fantasy RPGs are especially guilty of this when they start defining magic systems so interwoven with the central rules that if you take it out, the whole system collapses into an unplayable mess. For those reasons, I think the ideal RPG would have complex rules and very simple dice rolls. Ideally, one single roll.
So why should that one roll use ten-sided dice? Well, it's partly mathematics and partly convenience. Convenience, because some dice are simply "better" at giving random results than other. For one, the general shape of a die influences how well it rolls. I admit, this is a very subjective point, but from my experience, d4s and d8s are very bad in this regard due to their very angular nature. This would imply that the less angular a die is, and the more faces it has, the better it rolls, but there's more to it than just that. You see, most gaming dice aren't exactly fair. They're made in a device called "rock tumbler". Those interested can research the whole process in their own time, but for what I'm saying here it's only important to know that the end result is a die with rounded edges that is more dense in certain parts. While this irregularity only poses as a very small influence on the randomness of that particular die, it's still there and the easier it is for the die to, in physics terms, change from one state to another, the bigger the influence is. This phenomenon is particularly noticeable with hundred-sided dice (yes, they exist, although they're made using more fair methods), but it's mainly a big problem with modern twenty-sided dice. For example, my good ol' purple d20 tends to land on 18 and adjacent numbers (2, 4 and 5) more than anything else.
Following the above logic, the best choices for our one true die are d6, d10 and d12. So why do I choose the d10? As I said before, mathematics. In the most simple case, a one die roll, I don't think the scale of 1-6 is large enough to allow for convenient division. In a simple success/fail case, the probabilities only move in sixths, and the problem only worsens in cases where we have multiple results. In this regard, the 1-12 scale is clearly superior, because it's divisible by 2, 3, 4 and 6. So the d12 sounds like an ideal candidate, and in a way it would be, were I not human. But I am, and as a result I'm primed to think in base-10, which makes operating with numbers between 1-10 much easier, which comes in handy when you need to roll more than one die, not to mention that humans just instinctively understand the scale of 1 to 10 better than any other. There's also the ability to perform a so-called "percentile roll" (d%) that provides you with a scale of 1-100.
In terms of major RPG systems, at least those that I'm somewhat familiar with, d10s are important in Vampire: The Masquerade, and probably other World of Darkness systems as well, with what I think is a very beautiful roll mechanic, where the player's stats influence not an additive modifier to the roll, but rather the number of d10s that they roll. I have seen versions that use d6s rather than d10s, but I believe that was a homebrew "hack" of the game, not any official version. There are other major systems that utilize different kinds of dice, for example GURPS (d6) and the d20 system (guess), so don't think that the d10 is unviersally revered as the Jesus of dice. This is all just my opinion, so feel free to disagree.