I typically take readings for each runnings, but they are only useful if you also know the exact volumes of each. I use the gravity of the runnings to predict my pre-boil efficiency before I am done sparging, particularly for higher gravity brews where extract efficiency tends to suffer. If I see I am undershooting a bit, I adjust my sparge water volume to collect some additional runnings and boil a bit longer to reach my target gravity.
Of course, if you only get the gravity of all the runnings, you can still adjust your target gravity with some DME or water, as necessary. That's the easier method, IMO. Also, if you were comparing the accuracy of measuring gravity using separate runnings vs. the combined runnings, the latter would be more accurate since you only have one (large) volume of wort to measure and only one gravity measurement (less room for human error than three separate readings).