Implement a Stopwatch
Python 2, 167 129 bytes

-36 bytes mostly* from using Maltysen's idea of catching ctrl-c using an exception - go give credit!
-4 bytes thanks to DLosc (init n and b to 0 rather than f())
-1 byte thanks to FlipTack (use p^=1 rather than p=1-p)
-2 bytes thanks to Felipe Nardi Batista (remove precision specifiers)



import time
f=time.time
n=b=p=0
while 1:
 try:n=[n,f()][p];t=n-b;print'\r%02d:%02d'%(t/60%60,t%60),
 except:b=[b-n+f(),b][p];p^=1


Works the same as my original, below, but with the control key sequence of ctrl+c.
(Tested by me with Python 2.7.8 on Windows 7, 64bit;
Tested by Brian Minton with Python 2.7.13 on linux, 64bit)

* also collapsed if statement to a list lookup in order to get the try as a one-liner.

My original:

import time,msvcrt as m
f=time.time
n=b=p=0
while 1:
 if m.kbhit()and m.getch()==b'p':b=[b-n+f(),b][p];p^=1
 if p:n=f()
 t=n-b;print'\r%0.2d:%0.2d'%(t/60%60,t%60),


(Tested by me with Python 2.7.8 on Windows 7, 64bit - this code, however, is Windows specific due to the use of the msvcrt library)

The control key is 'p'.

n and b are initialised to the same value at start-up, giving an "offset" of 0; p is initialised to 0, indicating a paused state.

Whenever the control key is pressed the value of p is switched. When switching from a paused state to an active state b is updated to a new value keeping any current offset from the previous active state(s) with b-n.

During an active state n is repeatedly updated to the current time by calling time.time().

The difference between n and b, t, is then the total number of seconds (including a fractional part) elapsed during active state(s).

The minutes elapsed are then t/60 and each of the minutes and seconds are displayed mod 60 with (t/60%60,t%60). Leading zeros are prepended for each using string formatting of the integer part with '...%0.2d...'. Printing a tuple (the trailing ,) where the first item has a leading carriage return (the \r) causes the previously printed text to be overwritten.