PINE TREES
Description: Naturally one of the fastest-growing and tallest-growing trees in the game, this tree is best to be farmed for wood and sticks.
Grows Best: in my experience, the pine tree grows best mostly anywhere. The biggest I've seen have been at the equator, but that could be because that's where I always live.
Animal(s) Spawned by Tree: dropbear
Seed: Pine Cone (uses: planting, campfire/kiln fuel)
Pine trees are by far the best trees to farm for wood and sticks, partially due to the fact that they grow quickly and tall, partially because they can live long, the only problem is that they spawn dropbears - so light up your farm and kill the dropbear with an iron sword! They don't need much pruning, if they have adequate light they can grow very fast, and basically cut them down whenever you feel ready. Generally, it's best to wait until you have gotten 20-40 pine ones from the tree first. Usually pinecones grow at random intervals, and not in batches like some fruits grow.
MAPLE TREES
Description: Second-tallest, second-fastest growing tree. It seems that the main reason of a maple tree is because of its growth pattern and looks. Its seeds are almost useless.
Grows Best: usually in between an equator and a pole, I think.
Animal(s) Spawned by Tree: none
Seed: maple seed (uses: planting)
Maple trees are a relatively good tree to grow if you either don't want to grow a pine tree (which is understandable, these are better to grow if you don't want dropbears). They still grow quickly and rather tall, although not as tall nor as fast as a pine tree grows. They're easily manageable, not as wide, and still produce plenty of branches for sticks and logs for wood.
Edit: maple seeds are edible in 1.4!
COCONUT TREES
Description: A tall tree, the taller this tree is the more coconuts it grows on the highest branch at any given time. The coconut tree doesn't grow many branches.
Grows Best: Equator
Animal(s) Spawned by Tree: none
Seed: coconut (uses: planting, eating)
The coconut tree, grown best at equators, is a relatively-fast-growing tree. It grows straight up, and gets only a few branches, which grow at the top. On the very highest branch, coconuts will spawn in "clusters" of multiple at a time, the amount generated defined by the height of the tree. Coconut trees can be grown in sand, compost, or dirt, unlike most trees which can only grow in compost or dirt.
COFFEE CHERRY TREES
This is going to be a big topic.
Description: The infamous coffee cherry tree, grown throughout the world for energy to the tired, food for the hungry, and the ability to live without sleeping. These trees grow slowly, and can die young if not tended for properly. However, they are probably the best trees to grow, if you have the time.
Grows Best: Equator (elsewhere and they grow MUCH smaller)
Animal(s) Spawned: none
Seed: coffee cherry (uses: crafting green coffee bean, indirectly crafting coffee, eating [food, energy], planting, etc.
MANGO TREES
Description: Trees grown easily for food. Generally their growth pattern is similar to a cross between a maple-tree's growth pattern and a pine tree's growth pattern, I think. Mangos can also be crafted into a yellow pigment.
Grows Best: near equator
Animal(s) Spawned: none
Seed: mango (uses: planting, eating, pigment)
Mango trees don't have much to be said about. They grow food, they work well if you live at or near the equator. And, of course, you can craft a yellow pigment from the mangos (thanks Nelson)! If anyone can think of something I should say here, post it and I'll try to add it.
CHERRY TREES
Description: DODO's! Must I say more?
Grows Best: between a pole and an equator
Animal(s) Spawned: Dodos
Seed: cherry (uses: planting, eating)
Cherry trees don't grow best, but they can spawn dodos I think. Honestly I think apple trees do better though.
APPLE TREES
Description: EVEN MORE DODOs! Yay!
Grows Best: between a pole and an equator (closer to the pole I think)
Animal(s) Spawned: Dodos
Seed: apple (uses: planting, eating)
Apple trees mass-generate dodos. They grow better in cold places, where it is sometimes snowy and sometimes not. They also grow apples.
LIME TREES
Description: food for mining - limes trees don't generate originally in a world, but you can get limes from mining limestone.
Grows Best: kind of near equator, I'm not entirely sure since I don't grow them too much.
Animal(s) Spawned: none
Seed: lime (uses: planting, eating)
Lime trees are a rare food to find when mining limestone. When you walk around a world originally, or at any given time unless you planted limes, you will find no lime trees. Don't rely on them for food while mining, though, unless you packed extras. You get an achievement for getting one.
ORANGE TREES
Finally, almost done!
Description: A normalish tree that grows oranges. Good to grow if you need food.
Grows Best: anywhere warm (and aboveground)
Animal(s) Spawned: none
Seed: orange (uses: planting, eating)
A good food to grow and eat, and they don't die all too fast either. Very good source of food unless you live where it's freezing 24/7.