I forgot to add that I learned to play guitar in drop C. The first band I ever learned songs from was System of a Down, off their first two records. So playing in standard is a little foreign to me.
I use it mainly for different power chord voicings, inversions, and large chords that just aren't possible in standard tuning. It also allows me to play in six-string standard (although in my case it's a half-step down) when it's needed.
Dropping a seven string leaves you with the possibility to play standard tuned and drop tuned pieces on 1 guitar. Standard E, and dropped A (unless you're further dropping all strings as stated above, in which case standard Eb and drop Ab).
Thinking in this way helped me acclimate to the seven, though after you wrap your head around whats actually going on you'll be working outside of the self imposed "box" that approach assumes.
As a lot of others have said, I use drop tunings to give me more chord options. Since I can make an octave powerchord with a single finger, it leaves me three other fingers to add alternate voicings onto a simple powerchord or play a melody over top of the chords.
As everyone else has said, it definitely helps with playing power chords and moving them around quicker and cleaner. Playing wider intervals like major 6ths / minor 7ths is easier too.
One of the disadvantages however is that playing close intervals like minor 3rds (which sound nice n evil down low) is a bigger stretch and usually a bit impractical.
I used to do it for the power chords, and you know, it allows you to get a heavier sound without tuning your whole guitar down.
But my musical approaches have changed since then, so now, I'm in for the interesting wide chord shape variations (Try tuning down to drop D, then play 6th string/2nd fret - 5th string/3rd fret - 4th string/5th fret, and tell me if you've ever heard a minor triad like that in your life. ) and also the wide intervals you can easily get, especially between your 6th and 4th strings like 9ths or 10ths...