Like a lot of smartphone owners, I use mine as a music player. When I got my Droid Incredible, though, I was really disappointed by the stock players that were on it, mainly because I listen to a lot of music and am consistently hunting down new (and old) stuff and sharing what I'm listening to with my friends and family.
The stock players are not designed for me; I get that. So I turned to the Android Market (the most poorly organized store in the world) to find something better. (I ended up searching on GetJar and AppBrain, too.) The slideshow below includes the results of that search.
For people like me, with large music collections, the desire for better sound quality, broader format support, and some customization options, I recommend PlayerPro, PowerAMP, and Audiogalaxy. Although, as a platform, the new Amazon Cloud Player is pretty great for just about any type of music fan.
That's only four of the 10 I tested, though, so if those don't work for you, check out the rest in the slideshow. Also, most of them are free; PowerAmp is the most expensive at $4.99 and worth it. And if there are any I missed that you think I should add, please let me know.