using the 'other' hand
Generally speaking you need two hands to play guitar. I'm right handed but yet I know that when I'm playing I WILL be looking at my left hand. It's got the most complicated job of fretting individual notes and chords, of performing string bends, hammer-ons, pulloffs, vibrato and generally having the harder time of things. The vast majority of guitarists that I teach are of the same mindset as well. When I was learning I pretty much focused entirely on my fretting hand because I was so overwhelmed by everything that was going on with it. So much so that I forgot about my right hand, my picking/strumming hand.
Never underestimate the importance of your picking hand. This is the hand that is not only responsible for making the notes sound but also when then sound and how they sound. It's a huge deal. After I had been playing for 10 years or so i started taking lessons again and for the first 6 months of lessons the teacher took my picking hand back to basics and had to teach me to play correctly with it again because my picking technique was so terrible. Because as guitarists we are so fixated with what is commonly our weakest, least dexterous hand doing the most complicated and taxing job we overlook the role that the picking hand has to play in things. In my case I was severly limiting what I could do and I'm gratefull that I took the time to correct things.
This does not have to be simply related to playing faster, quicker, cleaner etc but can also affect the most simpler things such as strumming. Grab your guitar and look at the following example of a strumming pattern. In case you were wondering, 'D' means strum down and 'U' means strum up!
1 + 2 + 3 + 4 +
D U D U D U D U
This is a very basic strumming pattern. You strum down on the beat and strum up between or 'off' the beat. It's not particularly interesting but also not particularly hard to do if you have a basic grasp over strumming. So, what about if we flipped it around, does this sound right?
1 + 2 + 3 + 4 +
U D U D U D U D
Now we are stumming up on the beat and down on the off beat. Should this make a difference?