Alternate picking is essential in my opinion, unless you want to play very simplistic music. Not that there's anything wring with that, as long as it's composed well....
But I've found alternate picking to be extremely helpful. Even some lines that are relatively slow can be played much more cleanly with alt picking. Picking hand speed is like an exercise in stamina and accuracy. Alt picking helkps that by cutting the speed in half and decreasing the need for accuracy in terms of downpicking(thought it increases the need for accuracy in terms of alt picking). It tends to give a fluid style to your sound if done correctly, as opposed to the almost triggered feel of straight downpicking.
Anyway, I recently came across an awesome lesson that has helped me with my picking. I haven't practiced it much (because it's so damn hard) but, I hope to master it in the near future. It'll will improve your playing immensely. Despite not having mastered it, I know it definitely will.
the task:
Practice songs you like using upstrokes only. upstrokes for riffs, solos, whatever you hear the guitar play. It'll confuse the hell out of your picking hand for a while (it still does for me), but if you're adept at downstrokes already, and can do this, you'll be on your way to mastering the guitar!