Adding to George's list:
Wheels
I check the wheels every few years for rim wear and spoke tension/wheel truth.
Just done a fairly extensive overhaul on my old 650B utility bike. The rear rim is at just over 14,600 kms and starting to get a bit concave, but I reckon I can still use it for a year or two. Front rim doesn't seem very worn at 9,500 kms, unlike the older rear rim it has a wear indicator. Both rims were still true, so no need for any spoke adjustment. Rims wear relatively quickly on this bike as it is my preferred choice for local riding in bad weather and/or on tracks and paths. I use the front brake more than the rear, but rear rims wear more quickly, probably because the rear wheel picks up more muck than the front.
Front hub is a SON dynohub, so I don't do any maintenance other than cleaning the outside. Rear hub is an old Sturmey Archer S5/2, so I stripped that down, cleaned and relubricated it. It still works well after 56,000 kms.
With a Rohloff, I would just check the flanges, as these can sometimes crack. Not had this happen on any of my hub gear bikes, but in 1978 I did crack a flange on a derailleur hub falling on ice.
Transmission
The chain hadn't been maintained for two years, so I took the ChainGlider off, wiped clean the chainring and sprocket, swapped the chain for another and cleaned the inside of the ChainGlider before refitting it. The latter had picked up a certain amount of black gunk, probably from a mix of dust and chain lube. The chain I took off was black, but not measurably worn, so I cleaned/relubed it and it will be going back on next time I do an extensive overhaul.
Pedals and bottom bracket unit didn't need any maintenance. The gear cables and housings had only been on for a few years, and still worked smoothly, so I didn't replace them.
Brakes
I dismantled, cleaned and regreased the cantilever brakes, but I needn't have bothered as the grease on the insides was still good. These brakes had been on the bike for 35,000 kms. The old Deore XT brake levers from the early 1980's (64,500 kms) just needed a squirt of silicone lube and very slight tightening to reduce play. The brake cables and housings had been on the bike for more than twenty years, so I replaced with new, the rear inner cable was a bit rusty so I should probably have done this sooner. I replaced the brake pads, which had been on the bike for about 4 years, they were very worn.
Headset
Dismantled (except for the fixed cups), cleaned and regreased. This is a Stronglight X headset with needle bearings with 51,000 kms of use.
Stem/bars and seat post/saddle
Took the stem out of the fork, seat post out of the frame, put some anti-seize grease on them and refitted them. The Tange straight handlebars (steel) had a bit of rust after 55,500 kms but not too bad so I didn't change them. The Ergon handlebar grips were worn, so I replaced these with ESI Fatty grips, which don't last so long but are a bit more comfortable. The B66 Champion saddle (69,500 kms) just needed its regular treatment - I use Nikwax rather than the recommended Proofide.