Dense = +somewhat large number of "blocks" to the pipe's distance
Vacuum = sets a negative value of "blocks" to the pipe's distance
Round-Robin = Well, I do not know how to explain this well but I guess most people know what Round Robin is?
The dense pipe is when you want items to go anyway but that way unless all other output slots are filled.
Like if you had a sorting system set up with a overflow chest next to the start of a pipe network and want it to only get filled if all the other possible output points are filled up. en
You would connect the pipe network to the overflow chest via the dense pipe. This way items would go strait to the chest rather than waiting for the items to bounce back from the end of the network after checking each output.
You could then redstone up a system connected to that chest to, say turn off your quarry.
The vacuum pipe is when you want to force all items to go down a pipe unless the output is already filled.
This can also be used as in the above example only instead of connecting a dense pipe to the overflow chest you would hook a normal pipe up to it and the vacuum pipe to the rest of the network.
Both examples could also be used to keep a chest filled with cobble from you network and trash the excess.
Round-Robin pipes attempt to evenly distribute item to available output pipes.
Going from the first available input then to the next, then to the next, and eventually back to the first pipe to start the sequence all over again. This is for when you have say multiple identical machines and you want to spread the processioning of item out among them. Or have say multiple solid fual boilers running and you want to evenly distribute the fuel among them.
These examples are basic ones but the most commonly used.
And encase you didn't know the normal, vacuum, and dense item pipes are designed to replicate some of the unique functions of the now defunct (as in the mod's author has vanished off the face of the earth and no mod pack maker is likely to trust her to keep her mod updated even if she did update now.) redpower mod.
And the round robin pipe is based on one from the additional buildcraft pipes mod. A great mod in it's day but as now more or less become redundant do to improvements and additions to various other mods. (No disrespect to what was and still is a fine mod and it's author/s.)