Making your own jumprings is fast and fun, and certainly more economical than buying them. Another benefit when you make your own is that you will always have just the right size ring for the project you're working on!  :)
All you need to make your own rings is:

2.*) a mandrel
3.*) a good flush cutter

* see notes at bottom of page
I use a portable drill to wind the coil of rings, but of course this can be done by hand too. Although doing it by hand is time consuming, and I can never get the tension just right so that all the rings are the same.

Anyway, to begin, start to wrap the wire on the mandrel, with the wire going over the top towards you.
Now put it in the chuck of the drill and tighten it down as tight as you can.
Pull the trigger slowly at first, guiding the wire with your left hand so that the coil is nice and even. As you get more practice, you can wind at high speed, and make a coil of rings in seconds!
When the wire reaches the end of the mandrel, remove it from the drill and clip the end from the spool.
You now have a nice coil that looks like this.
Take your cutters and cut off one ring at a time.
Now go make something fabulous with all those rings!  :)
Wire: The gauge of wire you use depends on what kind of project you're doing.  When you visit different chainmaille sites, you will see references to 'AR' (aspect ratio), 'ID' (Inside diameter), and 'OD' (Outside diameter).  You'll have to learn about these on your own because I never pay to much attention to them. lol I just make my rings in the size I think will work, and go for it!  But some patterns will require specific size rings, so if you plan on doing patterns you find online or in books, you should familiarize yourself with these terms.  :)

For making jumprings to use at the ends of necklaces, etc., one important thing to remember is that the larger the diameter of the ring, the weaker the ring will be. So you might want to make them smaller using a thicker gauge wire so they will stay together better.
Cutters:  There are many different cutters on the market that range in size, price and cutting ability. Some are rated to cut up to 20g wire, some can cut up to 14g wire, etc.  The two most important things to look for when buying cutters for making jumprings is the gauge rating and that they offer a 'flush cut'.  This will ensure that your rings will meet well at the cut. Some cutters that don't have a flush cut will leave a cut at the end of the wire that looks like this -><- You can see that with a cut like this, the ends of the rings won't meet up nicely.

I use Xuron ultra flush cut cutters  and they work great. I ordered mine from an electrical supply site online. Do a search for them, and then you can compare prices. :) (I don't see the exact ones that I ordered, but that doesn't surprise me since I got mine years ago. Any of the ultra flush cut shears they sell will work. )
If you really get into making chainmaille, and don't want to hand cut all your rings, you can either get a jeweler's saw, or buy electric cutters that will whiz right through the coil in seconds. You can find directions on how to use a jeweler's saw here.
At the Ganoskin site
At the About Jewelry Making site
Tammy Powley (the head of the About Jewelry Making site) has written an excellent article on everything you'd want to know about jump rings.
Now that you know how to make rings, and how to open and close them, what will you do with them?  Here is a terrific site with lots of info, patterns, links and tons of eye candy. Maille Artisans International League
Have fun!
There are different jumpring making systems, but the one I use is Dave Aren's 'Koil Kutter'. You will need to have a dremel type tool to use his system, but it works like a dream.  You can contact Dave at his email address and he will send you information on his system. :)
Mandrel: You can use different things for mandrels, (like knitting needles) or you can buy mandrels that come in specific sizes that are perfect for making chainmille. I got a set of three mandrels in different sizes at Wigjig and I didn't need to have any different sizes for quite a while. As I got more involved in mailling, I needed more sizes, so I got a set of 20 that Dave Arens sells. He doesn't have a website, but you can reach him at his email address.
I decided to add this picture because so many people have written to me asking me what tools I use, how I hold my work, etc.  

A lot of people use two pairs of pliers but I like to hold my work with one hand, so I use a jumpring ring on my left index finger, and only one pair of pliers. For me, it's most comfortable to use a bent nose plier, but that's an individual preference.

The jumpring ring has slots in it (for working with different gauges of wire) so you just put it on the end of your finger, pick up a ring with the pliers, slip it into the slot and give it a small twist to open the ring. Then use the jumpring ring to close the ring after you've attached it to your piece. Easy!

You can get these rings at various places. I got mine at Fire Mountain Gems,  but Urban Maille has them too, and I'm sure you can find them lots of other places. :)