VC, just to add a little to BOAC's reply (and I'm sure many more will come), there is a point during take-off at which the aircraft will be able to continue to take-off and fly, even with the failure of an engine. It could well be that the aircraft is still on the ground, but it makes sense to get into the air at that point rather than try and stop on the runway that is left. The aircraft will fly perfectly well and the crew than have plenty of time, after the initial adrenaline rush, to sort it all out and make preparations to land again.
Just out of interest, the 737 has two independent hydraulic systems (purists, I've left the standby out of this) and will fly perfectly well with one failed and adequately with both failed, three electrical generators and will fly well with two failed and adequately with all three failed, three sources of pressurised air and can operate normally with only one of those working.
Basically, aeroplanes are incredibly robust, and the statistics prove it. However, I can sympathise with you. My grown daughter cannot understand why I do this job, and when I travel with her I have to be prepared for the gripping of my arm during take-off to almost draw blood.
Hope this helps.