What gadgets or devices have you used to help manage wires or cords at home for the entertainment system are and for the home office?
It's by no means an all-in-one solution but I've personally found Velcro Cable Ties to be INVALUABLE. You can reuse them over and over; great for those "oh darn!" moments when you need to remove or replace a cable.
For home office I am a big fan of the Ikea Signum. It is a wire basket, with hooks for wires that attaches and hangs under a desk. What I have done is zip-tie a power strip to the underside of the basket, and route all of the wires up into the basket, then route as much wire as I need up to items on the desk (computer, monitor, printer, etc..). It works quite well, and takes care of the wire mess. I also use zip-ties liberally to bundle wires.
For a home entertainment system, I have had good luck with routing wires down the back, and using zip-ties.
I use a velcro cable wrap (this one, actually) for anywhere visible (on my desk behind my monitors, and upstairs in my living room behind my TV). It's a braided sleeve which has velcro running the entire length, which wraps around a bundle of cables. It's relatively easy to add/remove cables to this, and it's also very easy to allow individual cables to come out at any point along the length of it to go to where they need to go. This lets you have a nice looking black "trunk" that passes by everything and contains ALL cables.
I found it at a local store one day for <$1/ft, so I bought a bunch. Obviously the pricing varies - one of the places I linked above has it for $44, and it's not worth that much. This store has some other similar products.
For non-visible stuff, I'll echo others here, I just use velcro ties, twist ties, or zip ties, depending on how permanent it is (and what I have on hand). Zip ties are terrible to use behind desks or entertainment centers, because you have to cut them to remove/add cables and that is often difficult in a cramped space.
I keep my entertainment system on wire shelves, so most of my cables are tied to the posts / legs of the shelves. Of course, I also still have an old CRT television.
For much of my networking gear (power distribution, DSL modem, network switches, wireless router, small server, etc.), I have it mounted to a sheet of plywood in the basement along with the punch block and patch panel for the house. I've got cable tie mounts screwed in, and then old-fashioned plastic cables ties. The only thing that's not wall mounted is the old VGA 9" monitor (640x480 in 4 bit monochrome!), keyboard and the UPS.
For office, well, I have another set of wire shelves in the closest room that I have in there, but I take stuff off the shelves as needed (scanners, sewing machine, embroidery machine, etc). The cables are either tied up with velcro straps with the slots in them or with twist-ties (that are actually pairs pulled out of the scrap left over from running twisted pair (eg, CAT5 of better, but it has to be solid, not stranded like what's in patch cables)). My main computer these days is a laptop, so I only use that room for scanning, or when I need to hook up to a larger display.