(Some of this I started way before the whole pre-term labor thing started...but that's beside the point)
Basic, and pretty intuitive chain mail weave. Some tutorials can be found here and here. It's actually one of the first things that I made a bracelet out of and actually completed.
The rings I purchased at Michael's...the one I go to is pretty limited on the color and size choice on these things. These are made by Darice, and are actually quite "cheap", as in they bend quite easily with your fingers, and the ends aren't as nice and polished as ones I purchased later. As I mentioned, the sizes were quite limited, these were the largest ones, just marked as being 12mm. Not a wire gauge, not an inner diameter measurement, just 12mm.
Another European 4-in-1 bracelet, but just a little wider. The intent was to make kind of a cuff-style slave bracelet, which I might still do.
These rings were ordered online, also made by Darice. They are the next size down from the ones above at 10mm (once again, no inner diameter, no gauge). I actually like the size of these the best out of all of the Darice rings. Unfortunately, they are still quite "cheap" (can't tug on them too hard or they'll bend out of shape!) and apparently that size is not very popular, and many of the single color packs aren't available anymore.
The last of the Euro 4-in-1. This one is so shiny and pretty, overall, more my style (and I have worn this a few times...I love it!).
This is one of the first things I made when my brand new, shiny, wonderful rings arrived from The Ring Lord. These guys are much more uniform and "solid", requiring manipulation with a set of pliers instead of your fingers (unless you're really strong and don't mind the marks left on your fingers from trying to bend them!). They also close very flush, and have no little burrs on the ends. The outside rows are a darker green, the middle is a lighter green, although it's hard to tell. Ring size is 18 gauge, 3/16 inch inner diameter, saw cut.
Helm Weave (with silicon/rubber o-rings!)
And now for something completely different. Another pretty basic weave is the helm weave. It's not quite as intuitive as the previous, but it's still fairly easy to do. Some tutorials can be found here and here. The reason I started this was that I was curious to try out some rubber o-rings. After looking online, I decided that a basic helm wave might work well, since the rubber rings don't open and close.
This one is also considered to be a staple of chain mail, and still considered to be relatively easy and versatile. Byzantine makes a boxy sort of pattern that looks pretty interesting. Tutorials can be found here and here.
So I actually lie a little bit...this isn't a REAL Byzantine, but rather one half of it, and using a mini-mobius as a connector between the units. The result is that it isn't quite as thick or boxy as solid Byzantine. It was made with 18 gauge, 3/16 inch inner diameter, saw cut rings, which are quickly becoming one of my favorite ring sizes.
2 in 2 Chain
Celtic Visions Hexagon