I need to replace my rear wheel, and happened to get one for free that's 700x45c. I don't have any compatible tires at the moment though.

Tires that are more than 45mm wide are kind of hard to find around here, and the selection isn't good... how narrow can I go on this wide of a rim? Or do you have any recommendations for a good wider tire that's under $50? I mostly ride on paved/semi-paved town streets. Thanks!

Try for a tire about 1-1/2 times wider on the outside, than the rim is on the inside. There should be a decent selection, and you don't need to spend anywhere near $50.00 for quality bike tires. They may not be top recognized brands, and may be slightly heavier, but that doesn't mean they can't serve you well for general purposes.

FWIW, I use tires that retail for under $15.00 for my commuter, and they hold up as well as anything else might, lasting until a large glass shard makes a cut too big to repair.

Ah, that makes a huge difference!

I thought the tires had to be as wide/wider than the outside rim diameter. Being able to put 35's on really opens up more affordable options. Thanks!

1-1/2 times as wide as the inside should be wider than the outside. I doubt your rims are actually 45mm wide, maybe they're made for 45mm tires. Here's a link to a chart showing optimal tire/rim width ratios (scroll down)

Yeah, I went back and measured... it's actually about 28-ish wide. So the moral of the story is always check your measurements!