Not very much anymore, in the scenarios that you see in the movies.
It used to be the standard technique for "infernal machines" in civil disorder situations or criminal bombings, in order to preserve the pieces for forensics. Military ordnance (such as in the famous TV series "Danger UXB") doesn't tend to have exposed wires to cut.
However, in the 1970's the Irish Republican Army (IRA) started to develop bombs that were packed with improvised anti-handling devices (see for example http://en.wikipedia.org/wiki/George_Styles) and it simply became too dangerous: luckily the British invented something called a pigstick that allowed the components of the bomb to be separated without the need for cutting them open (see http://en.wikipedia.org/wiki/Bomb_disposal#Projected_water_disruptors). The noise it made as it went off was referred to for many years as a "controlled explosion".
Once the pigstick (and its many imitators) arrived cutting the wires became a very rare option which was relegated to a "when all else fails" option.
However there are exceptions. Booby trap clearance in tactical situations may require wires to be cut silently, and increasingly in Afghanistan for example operators may sometimes have to use "manual entry" because it is simply too difficult to carry the amount of equipment that would be needed to fire off repeated pigstick charges.
BTW the wires aren't necessarily colour coded – there is no international electrical wiring colour code for terrorists. The colour issue was probably invented by hollywood to introduce drama (I think the first time the red/blue dilemma comes up was in the movie "Juggernaut" in the 70s.)
Another example of hollywood fiction is the mine that only goes click when you stand on it (no such mine exists – see the definitive text "Jane's Landmines") and don't even get me started on "the Hurt Locker"...
BTW The suits referred to above are quite useless when actually at a bomb (the explosive force will turn you into pink mist when you are close up to a big bomb regardless of the suit) but is intended to protect the operator if approaching a device that is fitted with a timer.
I recommend entering Bomb disposal in wikipedia