You've basically got three sets of bearings on your bike: hubs, bottom bracket, and headset. It's pretty easy to check if the grease has been blown out of any of them by listening to them spin or by checking for play in the part. If anything sound gravelly when you spin it the bearing definitely needs some love.
The wiggle check is a little more drastic, but also worth trying. If your dropouts are tight and you can still wiggle the wheel by grabbing the rim, you need to repack your hubs. If you can wiggle one crank arm and the other wiggles, you need to repack your BB.
Play in the headset is probably the biggest risk, because a sloppy headset is one of the few maintenance issues that, left unchecked, can actually ruin a frame. If there's slop in your headset and you ride the bike, the impact of the steer tube rocking back and forth can ovalize your head tube, and then you're kinda hosed. So be really careful to check that your headset seems solid. Turn the bars so the wheel is at 90 degrees to the frame and rock the bike forwards and backwards. Put your fingers on the interface between the headset and the frame, headset and the fork crown, and headset and spacers, and feel for any play. If it feels solid, you're good.