Tee Fire-Good to cook on as long as the top of the tee is not too wide for a pan or skillet to sit on. Regardless of how wide the tee is, it's a good fire to roast meat on in moderate to high winds. May be hard to dig in the desert where the ground is as hard as concrete.
Log Cabin Fire--Great when you need heat or light because it does both very well. However, it consumes a lot of wood, so have a good supply ready before you light the fire. This fire is excellent for signaling, because of the light it gives off while burning.
Long Log Fire--Another good cooking fire, as long as the burn area is not wider than your frying or boiling pan. You may have to secure both logs to keep them from rolling and remember, the two main logs will eventually burn as well and need replacing eventually.
Key Hole Fire--Good fire when winds are rough, because the base of your fire is below the surface of the ground. If you have a grill, you can place it over the circle as long as the hole is smaller than the grill, and cook. Good fire for moderate to fairly high winds.
Star Fire--The one I use often, no wood cutting needed, because you simply push the ends of logs into the flames. As each log is consumed by the fire, just push the end of a new log into your fire. It's easy but a little work to keep burning well. It's not a good cooking fire, unless you pull some hot coals away from the open flames to cook on.
Dakota Hole Fire--Great for on the plains when you don't want to be seen or during strong high winds. This fire takes some digging, and it's like a 'U' in the ground. The blue arrows in the illustration show you air flow. It's not a good fire in my opinion for cold weather because it doesn't give off a lot of heat and I had to almost sit on it to keep warm. Not easy to dig in frozen ground either, so keep that in mind.
Teepee Fire--The most common type of fire, but most often is made way too large. Dry woods can usually be broken into various lengths for burning and make sure you have your fire burning before you start to shape the teepee fire, unless you're an experienced outdoors person. This fire gives a lot of heat and light, but coals will have to be pushed to the side to cook with and I usually move them into an area where I have three rocks, like a triangle so I can place a pan on the rocks to cook with. With the hot coals in the middle of the rocks, the pan resting securely on the stones, cooking temperatures are easier to control.