I use the twice around the peg and through the hole method. I can often replace a broken string before the song is over using this method.
Unless I'm giving the guitar a good cleaning, I usually replace the bottom three, then the top three.
I hate the unbalanced sound of new and old strings on the same guitar so I replace a set at a time.
My used strings go right in the garbage when they come off the instrument.
I usually change them the night before a gig.
I find that guitars and octave mandolins need changing sooner than mandolins or banjos. My Autoharp strings have been on there for 7 or 8 years and I've never changed my piano strings. My wife has never changed her hammered dulcimer strings. I figure the more your fingers come in contact with the strings, the sooner they go dead. I've also noticed that some people seem to make strings go dead right away. Maybe their body chemistry? I have one friend who will play my guitar for ten minutes and the strings will be dead.

And to answer DrugCrazed's original question - Yes, I love playing new strings.