Technology has obviously come a long way. In fact, it is enabling us to store all the TV components, including the cable box, in a closed door cabinet behind the TV wall and still use the remote.
By the way, here's what the cabinetry in our butler's pantry looks like with the inside painted black. I had originally thought I'd need to cover the glass with fabric or wallpaper, but the black paint so completely disguises the TV components that I won't have to.
UPDATE FROM CHRIS:
Based on some questions with regard to types of IR transmitters and what I used, here are some links to the products:
The Extender Kit is The IR Extender Kit from Logitech:
This kit has everything you need to connect multiple devices to the main "receiver" point hidden near the front of your TV. You could use all of your existing remotes with this device, it just transmits the signal through. One comment asked if you could turn everything off at once, which would be unlikely unless you had a "learning" remote for your TV/Cable Box/Satellite that could handle all of your devices.
Because of this I chose to buy a universal remote so we have one remote for everything. I picked the Logitech Harmony One:
I would rate the remote 3/5 stars due to a difficult setup and cheap feel. The IR extender gets high marks, very easy to set up, 5/5 stars.