There's multiple reasons that come to mind... For some the male fans, they might appreciate her tomboyish side; it breaks away from the very girly, fru-fru nature of the show, and can make for some decent stories and situations.
For the girls... Well, I think it's partially the same reason. I'd guess it's because she's very outgoing, and doesn't give up. She's not a weak character in any sense. She'll do anything to help her friends in a time of need, and yet she's very independant. And that, in this day and age, is something looked up to greatly.
The bottom line is, almost everybody can relate to her in some way or another. That's good and bad in ways. Or at least in my opinion. It's good because... Well, because! If you can relate to a character, I'd think you kind of automatically like them, because you tend to like yourself, and if someone else mirrors you, you'd tend to like them as well. However, it's bad, because that's a sign the she's not too deep of a character. If she had an uber-unique character and a complex backstory and personality, I don't think as many people would be able to relate to her, as not as many people would be so similar to her, but she would be much more fun to watch.
So, I think the reason you see so many people, new to the fandom, with Rainbow Dash avatars and always using "20% cooler" and "10 seconds flat" is because, before watching a bunch of the show and discovering everypony else's personalities, some of which are wonderfully complex, they see this character that they automatically relate and attach to, and decide that she's the one for them.
...PHEW! That's one of my longer posts! Well, hope you enjoyed that piled-on mish-mash of everything but the kitchen sink... I know it didn't!
~BAWK!!!