If it's in projected coordinate system you could do a field calculation with Pythagoras relatively easily:
Distance = SQRT[ (X1-X2)^2 + (Y1-Y2)^2 ]
but I would hazard that there's no need if you have these spatially located already. Also if you want to do geodesics you will have a lot of fun with the Haversine formula.
I would convert your destination points to a separate feature class then run 'Generate Near Table'.
If this isn't an option if you have thousands of points a script could use the 'Near' tool, run selections on each feature, generate scratch outputs then merge them back into one feature.