I breifly discussed what key things you should look for in another post, but I figure I will provide a more complete answer here, broken down by opponent's race:
Zerg
Things to watch for:
- When does he build his spawning pool? An early Spawning pool (eg after 10 Drones) can mean a rush or early agression, where as a later spawning pool (eg 14 Drones or after Hatch) is usually a more Economic based play, and you should look for an expansion.
- When does he get gas? Early gas (eg before the spawning pool) usually means speedlings, possibly a quick Lair. If he gets his gas right after his spawning pool, this might mean some Roach play
- When does he expand? Almost all Zerg expand, but if he doesn't you maybe looking at some 1 base Muta play. If he does expand early (eg at 16 drones or after Spawning Pool) usually this means more Macrobased play looking for an economic advantage
Protoss
Things to watch for:
- What does he build after his first Gateway? If you see a second gateway, get ready for a early or timing push (usually 7 minute mark). If you see a Cybernetics Core, you may still be in for a timing push or a Cheese
- When does he get gas? A lot of Protoss will get their gas around the time of the Cybernetics Core, but if you see him getting both, that's a warning that he might be looking for Void Rays.
- Where are all his buildings? Protoss frequently like to hide Dark Templar Shrine and Stargate, so if you're in his base and you expect him to have more "stuff," start asking yourself "is he proxying?"
- Does he have an early Forge? Early forges can be a sign of cannon rushes, but a slightly delayed Forge can be the sign of Proxy Gateways. In both cases you're going to have to scour the map.
Terran
Things to watch for:
- Where did he build his first Barracks? If there is room for a tech lab, watch for Marauders possibly early Reapers.
- Did he rush a Factory? A lot of Terran players will go factory right after their Barracks. This usually signifies Hellions or Mech play, though sometimes its part of a 1:1:1 build
- How much gas does he have? Like Protoss, a lot of Terran will take a gas after their Barracks, so that's not unusual. However, taking 2 Gas is unusual and you should watch out for it.
This is not an exhaustive list, just some of the basic things to watch out for.