Damn, you guys must be really good players, if those songs define your playing. Interesting topic I must say.
Now, I couldn't really make a list of the songs I really sound like because most of my playing sucks. And if I wanted to show you my playing I'd record some of my own songs, not someone else's. Anyway, these songs represent fairly well what I'd LIKE to sound like:
Jason Becker - Opus Pocus
Hellborg/Lane/Vanyakrams - Mirror (the fusion of Indian and western music has been done many times, but never as good as, or anything like, this)
Iced Earth - Dracula (crushing metal rythms and harmonies just don't get any better than this)
Ayreon - Day 12, Trauma (I think this song shows Arjen's brilliance more than any other song, but I wish I could say the whole album. He's also a complete geek and will write a concept album about the quest for a whole peanut amidst the smooth peanut butter, but that makes him all the more awesome)
Dream Theater - A Change of Seasons (for obvious reasons)
Steve Vai - Answers (one of the happiest songs I know)
Megadeth - Symphony of Destruction (classic, straight-up yet catchy and melodic metal)
Marty Friedman - Triumph (many have done the anthemic, majestic style of playing, but never as passionate as Marty does on this song)
Steve Vai - Rescue Me or Bury Me (with hands like that it's easy to overlook his songwriting ability in favour of his incredible guitar playing, but this song is IMO the best pop/rock ballad ever written)
Al di Meola - Egyptian Danza (wailing les paul, baby!)