A workhorse rope is one that can take a lot of use and abuse. If you're climbing a route with rough rock and edges, this is your rope. It's thick and easy to hold onto, making it less likely that your belayer will drop you. Biggest drawback: less smooth traction.
These are the most popular ropes. They're the ones most people buy. These ropes are the perfect weight and are acceptable for just about everything, making them the go-to ropes for most climbers.
These are the newest "it" ropes to hit the climbing scene. These trendy, skinny ropes are ideal for long or complex climbs. When you've got a lot of slack or you need to turn over many belays, their light weight build is a blessing. They are a bit tricky to "catch" and needs a bit of practice before actually hitting a mountain. They also don't rub well against rougher terrain, but when it comes to hauling and belaying, the skinny ropes are pooching with potential.
These are a great option if you want to limit rope drag when speed is the name of the game. When it comes time to rappel, you can go twice as far by tying the 2 ropes together and two strands of rope also reduce the odds of your lifeline being severed either from a leader fall over an edge or from rockfall.
Twin ropes are another great 2-rope system to use when speed is important, only twin ropes are lighter and less bulky than half ropes.
Static ropes are not climbing ropes and should not be used as such. Static ropes don't stretch and should be used in rescue situations or when you are lowering, ascending, or pulling up a load.