I'd say once per year is enough for most riders, maybe twice for those who ride in lots of rain. Those with sealed (cartridge) bearing headsets don't have to bother, but note that sealed bearing cartridges can go bad and should be checked regularly and the cartridge replaced if necessary. General servicing involves removing the fork and cleaning the cup and race bearing surfaces in the bike's head tube, the fork crown, and the removable top race (that's 4 pieces). I just wipe clean with a rag, then spray with WD-40, then wipe clean again. Inspect for signs of pitting or divots. The bearings can either be cleaned or replaced. Most headsets will use 5/32 size bearings, but Campys use 3/16. Use a high quality thick grease, like Pedro's Syn grease, to repack. Put grease in each cup, on each race surfaces, and on the bearings, as you reassemble. It's really not a hard job and only takes 30 minutes, but be sure to readjust carefully and test ride. It should turn smoothly, without binding or stop points. If it jingles at all (bounce the front wheel on the ground) or the fork has play, it's too loose. If the steering seems wobbly or unstable it's probably too loose. A headset with divots may feel like it has a spring-loaded mechanism to always keep the handlebars pointed straight.

It's certainly worth checking the headsets of older bikes. I once pulled apart an almost-new headset and found 2 half bearings (this headset made noise whenever the bike hit a bump). You can feel the headset best by removing the front wheel and holding the fork near the crown while you turn the steering. Lack of grease is noticable. I was once helping a friend service her bike and noticed that the headset felt like it had no grease - I think it had never been serviced in 8 years. So I pulled it apart to regrease it. When I removed the fork from the frame, I looked at her face, and the expression on her face was as if I had just removed a leg from her best friend!