The sound is a combination of all factors like the quality of the guitar and pickups, the amp and the effects you're using. Even the cables contribute to a bad sound if they're cheaply made.

I guess it depends on what you're trying to get out of your sound.
One thing I found was that as soon as I added things like chorus, reverb and compression into my signal, it improved the sound a ton.
Like right now, for recording I don't even use an amp and the guitar is over 35 years old. All I do is put it through a Boss GT-8 Multi-Effects Unit and then maybe add some speaker simulation later on using a plug-in like Amplitube.

If overdrive is what you're looking for then a combination of that plus some compression will really improve things. Chorus kind of doubles up the sound a little and really helps a guitar that can't be tuned properly. The chorus in a Multi-Effects Unit will be in stereo so that will add to the sound as well.

Most importantly though... start with the best guitar, amp, and cables. Use new strings and an electronic tuner. If you want more 'sweetening' go in for a couple of pedals or just spring a few hundred bucks for a Multi-Effects Unit.

Here's an example for instance of taking a basic, under-average sound and using a few effects to sweeten it up:

http://guitartricks.com/lesson.php?input=10684

FYI: I'll be updating this lesson into Hi-Def this week so check back a little later and you'll have a much better quality video to look at.