Some rims have a little hole drilled in the side, when it disappears - time to replace. Modern rims last many 1,000's of miles. Just keep them clean.

I usually run 2 rear tires to 1 front, getting about 1,500 - 2,000 miles out of each rear. Although I don't run them as long as some. Once it gets really squared off (wearing down the center thread) I think about changing it. Some will run tires until you see the cords - not wise. I figure tires are cheap, and better then a crash from a blown tube. Worn tires seem to flat more often as the rubber thins, and little slices and cuts seem to open up over time. Some tires like Conti 4000 series have wear indicators as well, since many road bike tires are smooth, tread doesn't really give much of an indication.