Most bearings need cleaning and greasing after some time in use. Modern sealed cartridge bearings can run for years without maintenance, classic cups and cones need more frequent care. There are six bearing sets on a bike: front wheel, rear wheel, headset (handlebar axle), bottom bracket (crank axle) and pedals. The best tactic is to disassemble the bearings, flush out all dirt and old grease with WD-40 or similar agent, wipe dry with a cloth, pack new grease into the cups, place the balls into it using a tweezer and then assemble it all again. The cones should be tightened so that there is no play in the bearing and it runs smooth without much drag. New bearings can take slight preload which is good for them, old pitted ones can't (it's better to replace them). When tightening the cones, you need to hold three things at once: the cone, its locknut and the axle, usually by the nut on the other end. Find an assistent or a vise, or it drives you crazy :-).
A headset is mostly statically loaded, especially the bottom one which tends to collapse on some cheap BSOs (supermarket junkbikes). I saw it once: ball cage broke apart, all balls gathered on one side, the cup tilted, stripped the fork stem thread and damaged the headtube. The bike was totaled. My favourite trick is to remove the cage and put new balls all around the circumference of the cup, then there is nothing to break down.