Many of us here are composers, and so I was curious to people's techniques of coming up with their melodies. It varies from song to song, of course, but generally, how do you come up with your melodies?

I tend to find a chord progression and build a melody on top of it, though sometimes that's too restricting. I use the piano for the basic structure and then switch to string instruments for rhytms/harmonies. That or I just come up with it while sitting at the computer, though these tend to be less inspired.

Also, once you come up with a motif, how do you expand it into a full fledged melody?

I suppose trial and error? Usually I just stumble onto something. If it sounds nice, I keep it, if it doesn't, I discard it. I don't often obsess over whether or not I can improve on a melody. I do try to base it on a chord progression though. And if there are lyrics, I try to keep the restrictions in mind. Mostly I attempt to keep the melody sounding natural and flowing. If I can hum it, it's a good start.

I find that stumbling into melodies means that the melody is more natural, but it's harder to harmonize/modulate/etc than a "synthetic" melody (generally, at least).

I go through a couple of steps.
1. I think of a good sounding line to go underneath.
This could be a bassline, or a percussive line, or even a simple held chord.
2. I write in some other instruments/parts.
These parts fit in with the initial line, and are generally in blocks.
3. I write the melody around these parts.
With a great sounding backing line, the melody can fully express itself.
4. In go the harmonies...
Where is a melody without counter-melodies and/or harmonies?

Every single melody within each of my compositions is simply one of the haphazard, but lovely ditties *coughs* I hum as I pass between classes; luckily, I keep staff paper with me in my bag, so I can write that melody down just in case I forget it by the end of the day (having perfect pitch is SOOOO useful).

The hard part is coming up with a complex progression. I'd love to exploit strange progressions whenever I can, but I rarely ever find something that I consider "presentable." As a Romanticist, I'm not afraid to do something that the general public would recognize as intricate, but I also need to balance that with things that the public can easily relate to or at least find audibly pleasing. >_>

It's a neverending battle. ^^;