I notice when I go see local bands live they all have very nice tone to their guitars that sound very clean even when distorted and sound like the kind of stuff you hear in thrash bands such as slayer. I have a line 6 spider 3 and an ibanez VBT and it sounds like a computor, no crispy tone to it at all.

Any suggestions on good equipment that has natural, crunchy tone to it? (As in something I could use to play thrashy music)

thats why. i have one as well and i HATE it. i thought it was cool when i first got it, now i want a decent amp that doesnt sound like a computer and has a cab extension and effect loop... however, nobody wants the thing so i cant sell it.

basically, con someone into buying the thing and go buy a better amp. you wont get that exact sound you're looking for with a spider 3.

What kind of budget do you have to work with?

under $800 id say

Well you mentioned Slayer, so the JCM 800 is an obvious rec because that's what they use. However, I'd also look at a Peavey 5150 (the new ones are the 6505), because it gets the best all-around metal tone that can be found for less than $1000. I'm sure you could find a used half stack on craigslist in your price range, and if not you could also look into a Peavey XXX or a Mesa Dual Rec. Just try out a bunch of amps until you find the sound you want, then save more if you can't afford it quite yet.

this.

also, try not to settle for "good enough". keep trying stuff until you find EXACTLY what you want. you dont wanna spend several hundred on a new amp and then decide a week later that you dont like it.

Peavey 5150 - $400-600 on Craigslist/ebay/etc.
Mesa Rectifier cabinet - $400-500 on Craigslist/ebay/etc.

Keep in mind that the way to get a great sound like that is not simply to have really nice gear, but also to set it up in a way that sounds good. You need a lot less gain/drive/distortion than you think, and also having more mids helps a lot. Playing with a drummer and bassist add a LOT to your guitar sound.