Wooden Transport Pipes are used to extract items from a chest or other inventory. They cannot connect to each other and require power from a Redstone Engine or better to function.
Cobblestone Transport Pipes are the standard item transport pipe. They will not connect to Stone Transport Pipes or Quartz Transport Pipes. They have a high drag/friction which will slow items down once they leave a Golden Transport Pipe.
Sandstone Transport Pipes don't attach to machines. They can be used to connect Cobblestone, Stone and Quartz Transport Pipes together if placed between them.
Iron Transport Pipes will output only on one side. They will accept items from all sides. This makes them ideal for routing items down a specific pipe.
Quartz Transport Pipes have a low drag/friction so items passing through these won't slow down as much as they would through Cobblestone or Stone Transport Pipes. Quartz Transport Pipes will not connect to Cobblestone or Stone Transport Pipes.
Obsidian Transport Pipes will pick items up from off the ground. When provided with power from an engine the pickup range will increase. It will only work when connected to other pipes.
Emerald Transport Pipes are similar to Wooden Transport Pipes. They are used for extracting items from chests or other inventories, they won't connect to themselves and they require power from an engine. They have one more feature. They allow you to filter what they extract.
Liquid Transport Pipes
Nearly all the pipes mentioned above can be turned into waterproof pipes for transporting liquids.
Each pipe type can handle a different volume of liquid.
In order to transport power you will need to make yourself some Kinesis Pipes. Each pipe type can handle a different amount of power. There is no power loss over distance.