
So.... first off, why are there weaves and why so many weaves of CF. The simplest reason for most is that different weaves can either give varying amounts of strength and looks. they distribute forces in multiple directions differently and can often change strength in the way they are laid and molded as just for a different weave.
So lets just get into this and look at the first few weaves and the one's I have used. For a quick reference without looking at any data sheets (which I always recommend for the serious man), look at the pattern and see how many fibers go in each direction to determine the strength in that direction.
Also, you'll often notice something in the weave called 3k or 6k. This is essentially the fiber density per strand. higher density= stronger, but also heavier in a pretty direct proportion.

Plain Weave: which is just that, plain. If you've ever tried to make a simple piece of fabric or cloth, you've made this pattern. You can see it to the left. Like its right there and pretty big (its even 12k density to really show off, and a watermark cause I can't find a pic of my own to show the pattern well). Like seriously, if you can't make out this pattern then just stop. The over-under pattern is the most basic there is. This is pretty standard and works fine. Not the strongest of weaves but is solid and shouldn't let down. What I do love about this weave though is that it is the easiest to handle without making the fibers on the ends too messed up. Other weaves fall part incredibly fast, but make up for this is some cool patterns and more strength in the direction of the weave.
Now: the cooler looking one and still easy to handle(though not as much).
2x2 Twill weave
Now, as you can see, the pattern is over-over- under-under. Yet the amount of fibers in one direction is still equal. No real strength gain over Plain, but it gains a benefit for being cooler looking and easier to bend and mold into sharper corners. this is often the cosmetic choice for its unique look compared so as to stand out a bit more. Tell me if you have any more experience with this cloth being stronger than plain. I've used both of these weaves and noticed nothing than cosmetic and ease of molding differences.the funky, exotic, smexy, and odd weaves.
Now there are TONS of weaves, wayyyyyyy too many for this one post, but I'll go over 3 more. I have little to no experience with these so tell me what you think of these in the comments.
Satin Weaves (#HS)

These are supposedly some of the stronger structural weaves as far as I know. It is also pretty plain to see that the weave will fall apart in your hands if not handled well. Looks pretty cool though huh? for reference, the standards are 5HS and 8HS, the number denotes how many times a thread goes over the filler and then once over (5HS= 5 over 1 under 5 over, etc.)
Unidirectional
Ok, this apparently offers the Most strength in one direction, hence the name. Use this in applications where almost all of the forces exerted on the object come form one axis (up and down, left and right, front and rear). You can often buy this as a Tape of some sorts, even pre-peg (glue already in) to make a simple reinforcing sheet to a dent or so for repairs if not an entire weave.I don't like the look personally, but I'd like to see it executed well. Also, you see that weave perpendicular to the direction? This is probably Carbon Fiber, but some can even be made of fiberglass since it really doesn't add much strength. Again, I have no experience with this weave. sorry guys. not rich enough to play with everything, Yet!
Funky one
This is a twill weave, but instead of Pure Carbon, Kevlar is mixed in. It's supposed to be Impact resistant (huh, carbon already is for the most part). But Kevlar was often used as the light space age composite of choice before carbon Fiber. I can't remember (and Wikipedia isn't helpful today), but Kevlar has one of the best yield strengths (like 3600 MPa, that's 3600 million Newtons per square Meter if my Metric is right. Wiki says 3620 MPa).Now for some cool colored Weaves for that finishing touch.

Blue Kevlar Weave-------->

<-Holographic Weaves


