If you're playing rhythm guitar, as opposed to a lead line, the basic vocabulary of the guitar is described by the left hand and the chords that you're playing. If you think of a chord as a word, a chord progression as a sentence, and a song as being a very short story, that's the basic analogy that I'm desperately attempting to draw here.
Now if you only know three chords, say the perennial favorites, C, F, and G, there are only a certain number of sentences that you can construct. Add Am and you suddenly have the basis of the four-chord rock/folk progressions and a lot more things that you can say musically. But with only four chords, you're still likely to find yourself in a rut. So how do you get out of the rut?
Like English, the guitar has a number of ways of saying the same chord that sound slightly different. I can think of at least three ways of playing something that I'd call "Am7" at the first position and they're all differently nuanced, much like snow, sleet, and hail are all different words for "frozen crap falling from the sky when it's supposed to be spring". (Ok, so I'm a bit tired of the cold weather.) As you move up and down the neck of the guitar, there are more ways of playing Am7. So you can increase your guitar vocabulary by learning more chords and more ways to play the chords that you already know.
I have frequently joked about the Nate Bucklin Chord-of-the-Month Club, where each month, Nate will send you a new guitar chord to learn and use in a song. As far as I know, Nate will not send you guitar chords by mail. But there are a lot of ways that you can learn new guitar chords.
One way is to learn some new music by a performer that you like, whether a filker or a pop star. If you go to your local music store (or maybe your friendly filk dealer), you're likely to be able to find a songbook for guitar with chord diagrams in it. As you learn the songs, you're quite likely to add some new chords to your vocabulary that you'll be able to use in your own music.
There's also the Columbus System of Chord Finding -- otherwise known as discover the chord and land on it. If you're writing a song, you may well find that this chord isn't quite right and that chord is just wrong, but if you put this finger there, something good happens. Congratulations! You've found a new chord! And if you go to websites such as ChordFind, they'll -- probably! -- give you a useful name for it, so that you can call it something other than C^. (Sorry, catalana. :) )
Finally, there's the Mad Scientist Method. This involves picking up something that's not a properly movable chord form -- because it has open strings -- and playing it at some other spot on the neck to see what you get. Sometimes you get garbage. Other times, you get a perfectly fine chord. For example, the first-position C7 can be played quite happily at the 3rd and 5th frets. So can the first-position Fmaj7. (I must go higher than the 5th fret soon. Maybe next week...)
And with all those new chords, you've got a much better chance of getting out of your rut and finding something new to say.
Which is part of the fun.