When choosing a frame for a fixed gear build, it is crucial to understand what a rear dropout is and why a horizontal dropout is preferable to a vertical or diagonal (semi-vertical) dropout. You may also use a frame with track fork-ends if one is available to you.
Dropouts are the slots at the rear of a bicycle frame into which a wheel's through-axle is attached. There are also dropouts at the tip of each of the front fork lowers, but these do not play a deciding role in the fitness of a frame for conversion to a fixed gear.
The term dropout is derived from removing the axel from the fork-end. With a dropout, one needs only to loosen the bolts or quick-release on the axle, and the wheel can literally “drop out” of the fork-end slots. This quick removal is possible because the dropout slot is oriented either vertically toward the ground or horizontally in the direction facing the front of the frame. The chain will loosen and can be removed as the axle is moved closer to the bottom bracket and chainrings. Chain tension is typically achieved through a spring-loaded derailleur, but other tensioners exist.
Looking at a dropout from the side, you will notice that the slot has one of several orientations.
As on most modern bicycles, dropout slots may point almost directly at the ground when positioning the frame upright. This is called a vertical dropout. The image below shows a vertically oriented dropout:
Frames with vertical dropouts are poor candidates for fixed gear conversion because tensioning the chain relies on moving the rear axle away from the bottom bracket, increasing the distance between them. Attempting to increase this distance on a frame with a vertically oriented dropout, like the one pictured above, would require deforming or filing down the ear on the dropout…, which you should never do.
Dropouts primarily oriented toward the front of the bike are called horizontal and are the best dropout style for conversion to a fixed gear.
The image below shows horizontal dropouts:
You may notice that the slot on this dropout is not oriented perfectly horizontally to the axle-axle plane of the bike. Nevertheless, I consider this a horizontal dropout, and most fixie-tinkerers I've spoken with reference this style as horizontal.
As you can imagine, there are many frames where the angle of the dropout falls somewhere between the two pictured above. These are referred to as diagonal or semi-vertical. When assessing the conversion-worthiness of these frames, you need only ask yourself whether the slope of the dropout is little enough to allow for adequate tensioning of the chain. At a minimum, I would like to have ⅝” play and feel comfortable that the nut securing the axle will make complete contact with the dropout.
After building and riding a few fixed gears with dropouts, you may look for a frame with track fork-ends. Track fork-ends are similar to dropouts but with slots that receive the axle oriented backward away from the frame body. It is important to note that these are NOT DROPOUTS, regardless of what the rest of the internet believes. Removing an axle from a bike with track fork-ends requires loosening the chain and unseating it from the rear cog, and no amount of force will allow the axle to “drop out.”
Here is a beautiful example of Track Fork-Ends taken from the gallery:
In all honesty, it is primarily for cosmetic reasons. For many in the fixed gear community, myself included, there's a great deal of value placed on the simplicity and streamlined aesthetics of the bikes. Track fork-ends are sleek, classic, and logical. What they do not do is improve the ride-worthiness of the bike. So you can use them if you've got one but don't look down on a beautifully constructed fixed gear conversion with dropouts.
Be safe, and have fun!