You only need one wheel to have fun...

Should I get a singlespeed?
Yes, all the cool kids (myself included) are riding singlespeeds these days. Without giving you a long boring lecture about responsible spending, here's the rule: if you don't have some significant time on a singlespeed (meaning, riding on actual trails - not your cruiser around town), spending the money on a custom frame that is SS-specific is a very dumb idea. Will I take your money and build it for you? Well, yes. I'm not _that_ principled! But it's quite easy to find enough old parts and a junky frame to throw together a singlespeed for cheap (or free) and try it out first. Don't get caught up in what's cool - the only thing you should worry about is what will be the most fun for *you* to ride. For many people, that's a geared bike.

Ok, where do I find out how to build a cheap single to try out?
Try the MTBR singlespeed board. They have an extensive FAQ to guide you through the process. You do not need a frame with horizontal dropouts or anything fancy - in fact, it used to be a point of pride (before the current era of $3000 singlespeeds) to build a singlespeed entirely by dumpster diving.

What about fixed gears?
I'm the wrong person to talk to. I love my freewheel. And I really suck at riding fixies. But the folks at 63xc.com (the 63 is referring, I believe, to gear inches) can set you straight.

Ok, I want to know what my brake/chain tension options are for a singlespeed.
Now we're into the interesting stuff. There are a plethora of options, from free to big $, very light to very heavy, and highly functional to total junk. We'll skip the stuff that sucks for now, though.

Option 1: conventional vertical dropouts with derailleur hanger, external (bolt-on) chain tensioner.
The advantage here is obvious - you don't have to make any modifications to the frame to make your bike into a singlespeed. Cost is low, too - about $30 will buy you a generic-brand chain tensioner that attaches to the derailleur hanger. Add some cassette spacers ($10, or free if you scrounge 'em), an old cog (free), and maybe a bashguard ($20-50) if you want to remove the big ring from your crankset, and you're ready to rock. You can convert back to gears anytime you want, and you can use a rear disc brake without having any weird adjustment issues. Sweet! The downsides, though, are serious - the tensioner usually won't eliminate chain slap, chains are relatively easy to drop, and the tensioner itself tends to be a bit fragile. Weight is good, since the tensioners typically only weigh about 100 grams.

Option 2: horizontal dropouts with v-brakes
The lightest option. A typical horizontal dropout is 30 or 40 grams heavier than a vertical dropout, and you'll often need a BMX-style chain tug which attaches to the rear axle (another 20-30 grams). Also cheap - there's no upcharge for the dropouts, and the chain tugs are only $5 or so. Downsides exist, though - disc brakes are difficult to set up with horizontal drops, and there's no way to add gears to the frame without clumsy bolt-on derailleur hangers. I do offer a horizontal dropout that has a built-in derailleur hanger, though.

Option 3: Eccentric Bottom Bracket (EBB)
I will admit my bias right here: I don't like EBBs. They weigh a lot (add 1/2 pound to your bike for the shell and eccentric unit), they mess with the cockpit measurements (if you move the BB, you should really move the saddle and bars to keep the cockpit static, in my opinion) and they have a reputation for creaking, rusting, and generally being a pain. Also, since I only use the fancy Bushnell ones, they cost an extra $120. Ouch! Here's the plus, though - EBBs make it very, very easy to tension your chain without moving the rear hub or trying to get your rear wheel perfectly straight. Hence they allow the easy use of disc brakes and easy, quick wheel changes to fix a flat or change gears. For folks who don't care too much about weight and don't have sensitive knees that are going to react badly to moving the BB around all the time, they can be a good option. It's also worth mentioning that you can easily use gears, since you can just have vertical drops with a derailleur hanger on your EBB bike.

Option 4: Paragon sliding dropouts
I like these. They are a bit lighter (add 1/3 of a pound to your frame) than an EBB, they're stainless, and they allow you to easily tension the chain while using a disc brake. Easy wheel changes, check. Run geared or singlespeed? Check. Price? $120. The only downside (other than the price) on these suckers is that the jury is still out (they are very new) on long-term reliability and creaking/slipping issues. I have examined them pretty closely (and will have a bike of my own built up with them soon) and think that they'll be great. I've also heard nothing bad, but as of this writing, the darn things have only been available for 6 months, so nobody knows how they'll hold up for sure.