Types of Hives
2 Langstroth hives sitting side by side.
Warre' Hive shown here with the larger attic space on the top.
Inside photo of a top bar hive.
Top bar, outside view. Notice how the sides of the hive are on a slant.
Langstroth - Probably the most common type of hive used today, these hives are popular because out of all the hives they are the most standardized dimensions, meaning if you buy Langstroth parts in Australia, California or Michigan they will all be the same size and will work with your hive. These hives hold 10 frames in each box and stack and are easy to move, especially for pollination services. Generally made out of white pine and will need to be painting so the wood lasts longer.
Warre' Hives - Generally similar to the Langstroth Hives, the Warre hives are usually 8 frame instead of 10 frame. Most of the time, Warre hives are setup so the bees enter from the top of the hive and build their way down as opposed to a Langstroth hive where they enter from the bottom and build up. Warre' hives generally have a large lid on top, where the bees cannot gain access, that is used as a sort of attic to trap summertime heat and in the winter, you can add insulation to help the hive stay warm.
Top Bar Hives - These look like a saw horse and use only a top bar as a frame to allow the bees to "free form" their comb as it hangs off the top bar, hence the name. These hives costs a little more up front because you buy the whole setup at once, instead of having the ability to buy parts and pieces as the summer progresses. Some of the downfalls are: 1 - The bees sometime leave before they figure out how to build the comb off the top bars. 2 - Sometimes the comb falls off the top bar when you try and pull frames out. 3 - remember, none of these parts and pieces will fit or interchange with anyone else's hive, unless they have a top bar hive with the exact same dimensions (i.e. NUC won't fit either).
There are also other types of hives, many of which can comes in different shapes and sizes. All of the hives above work great and bees will be happy and healthy in them, it really is just about looks and personal preference.