Alright, here we go...
<span style="font-size:medium;]Wire Cutting 101
Blue wires are typically used as "patch wires", and added to circuit boards or wiring systems at the factory to correct design or fabrication problems. That is why Joe clearly pointed out that this would be the wire of choice to cut when attempting to stop a timer with 1.023 seconds left. These are typically used when rigging up timers to things that don't normally have timers on them.
Blue wires with a yellow stripe are slightly different, in that they are used not as a "patch wire" but as a connection to modular upgrades, such as automobile alarm systems. You would cut this one only if you wanted to disable an alarm from setting off. Especially useful at night when you don't want to wake the neighbors.
Black wires are of course your negative, or ground -- again, in typical 12-volt automotive applications.
Black wires with a white stripe are always used for "switched" connections, namely those associated with ignition systems or starters. This is the wire you would want to cut if you wanted to disable an automobiles ignition system -- or to gain direct access to the starter so that you could, for example... hot-wire it because you misplaced your keys.
I hope you manage to fix your coffee maker Sarge! 
Rick "Ripstick"
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