The fuzzy tape as you call it, is probably sleeving. You can use sleeving, heat shrink tubing, tape, split loom, or cable ties to bunch wires together.
You can hide wiress behind the Motherboard Tray, in a spare drive bay, or any place you can find.
You can get sticky back mounting bases. Either ones with the loops to hold a bunch of wires, or the kind that are flat and you cable tie them to the bunch of wires. You can use them to run wires in a certain area through your case. You can put them on the bottom or top of your case, to hold wires out of the way.
You can use flat cables if you want. Some people have the art of folding them, and can really keep them out of the way.
You can use round cables if you like the looks of them.
You could use a combination of flat and round, it's up to you.