You need to check
Enable Enemy Unit Selection, which is a new option unselected by default as of patch 2.0.4.
It's in options, under gameplay, the bottom-most checkbox on the right.
This will allow you to select enemy and neutral units in the map.
You may also be interested in changing some other new settings, see this thread on Blizzard's forums
Uncheck Enable Simple Command Card - Will bring back the good ol' command card with partrol, hold position, and all the other classic commands.
Uncheck Select All Larvae - Will allow you to click on a single Zerg larva, should you choose.
Check Enable Enemy Unit Selection - Will allow you to select enemy units and structures.
If you're a purist:
Uncheck Enable Starting Worker Rally - Will allow you to assign your workers manually at the start of a match, just like in previous versions of the game.
Uncheck Display Experience Points - Will stop the XP points from popping up over kills and such while you're in a match. (XP is still earned.)
Uncheck Always Show Worker Status - Will only display worker counters on "town halls" and Vespene Gas structures when cursor is hovering over it.