How do I protect against voltage surges from sensors?
A typical and simple solution is a schottky diode (low forward voltage drop) from your signal line to +5V (anode to signal, cathode to +5V) will limit the voltage spikes to a few 100mV above +5V.
Similarly a diode to ground (cathode to signal, anode to ground) can prevent negative swings. 

For something like a CT that is capable of huge voltage spikes, a TVS (transient voltage suppressor) instead or as well as the diodes might be a good idea too.

I would suggest a buffer (e.g. non inverting opamp, unity gain) in between your CT output and ADC. This would add a stage of protection before your ADC. You can use the diodes on it's inputs to protect it, and if you power it from +5V it is guaranteed not to swing higher than the ADC can handle. Also you could add a few gain taps (e.g. 1,5,10,etc) to switch between for different current ranges - this way you will be able to use the full range of the ADC better.
For instance your 680mV signal is only using (0.68V / 5V) * 100 = 13.6 % of the ADCs range. For an 8-bit ADC this equates to ~35 out of 256, 680mV / 35 = 19mV per ADC step (e.g. 00000001 = 19mV, 00000010 = 38mV, etc). If you had a gain tap of 5 (e.g 0.68V * 5 = 3.4V) it would be more like 4mV per step.