Look at the frame from various angles to try to determine that tubes are straight and aligned. Head tube and seat tube should be parallel. Seat stays and fork blades should be symmetrical. Check whether forks are bent back or twisted.
Check frame for cracks, bulges, or significant dents. Cracks often form on the down tube just behind the head tube. A bulge in that location is often a sign of a front end collision and might be accompanied by fork blades that are bent back. Also inspect for cracks in the bottom bracket shell. Check the drive side chain stay for excessive "chain suck" damage.
The headset should turn smoothly and without play.
A little surface rust here and there is generally not a problem.
Ask to adjust the seatpost and stem. This allows you to adjust the bike for a test ride and also permits you to ensure the seatpost and stem are not stuck, i.e. chemically welded or rusted in place, 'cause that's bad!
When you test ride the bike, you should be able to ride the bike no hands in a straight line without leaning to either side. If you can't, there is probably a problem with alignment or improperly dished rear wheel.
Spin the wheels and observe where the rims pass the brake pads to make sure they are reasonably true (within 1–2mm) both vertically and horizontally. Also listen and feel for roughness in the hub bearings.
Even if the wheel is true, be sure to squeeze all of the spokes by pairs to see whether the tension on the spokes is even. Flick spokes with you fingernail—the tone should be pretty consistent. A true wheel with very loose and super tight spokes is probably almost dead.
Check rims for cracks. Also, feel the braking surface—if an aluminum rim is significantly concave on the braking surface the rim is near the end of its useful life.
Tire wear is, of course, normal. For old mountain bikes a great upgrade is inexpensive (think Kenda) semi-slick tires to replace knobbies for riding on the street. Makes a HUGE difference in reducing rolling resistance.
The drivetrain should shift relatively smoothly. Look for bent, broken, or missing parts (to the extent you know what to look for).
Check cables and housings. Frayed ends are common. Fraying behind derailleur anchor bolts or cable stops probably requires replacement. Cable housings that are rusty, that lack outer casing, or have acute bends will also need to be replaced.
Replacement of a chain is almost a given so a dirty or somewhat rusty chain might not be a deal killer.
Check the chainrings while the crank is turning to see whether they spin true. Inspect the crankarms to make sure they are not bent or cracked. Check to make sure pedals are threaded in straight—otherwise they might be cross threaded, which might mean the crank arms would need to be re-tapped or replaced. Also examine the teeth on the chainrings for wear. Teeth that are worn out look hooked or like shark fins.
Grab both crankarms and pull back and forth sideways. Excessive play could indicate one of several possible problems. Pedals should spin relatively smoothly. Check plastic pedals for signs of cracks.
Brakes should operate relatively smoothly and, yes, cause the moving bike to stop safely. Make sure the brakes "return" after the levers are released. Failure to return indicates corroded cables/housings or weak, improperly adjusted, or brake broken springs. Inspect brakes and levers to see whether they are bent, cracked, or appear to be missing any pieces.
Check cables and housing as with drivetrain.
Brake pads wear and might need replacement. It's a good thing to upgrade them regardless.
I would avoid Pacific, Magna, Kent, Mongoose, Huffy, Columbia, and any brand sold at big box stores.
Fuji, Panasonic, Bridgestone, Miyata, Nishiki, Univega, Trek, Giant, Specialized, and brands sold at reputable bike shops are generally good quality bikes. Really, most bicycles that were made in Japan or Taiwan from the 1970s through the 1990s tend to be pretty good, or at least not horrible.
Schwinn, Ross, and Free Spirit are a mixed bag. The lugged steel bikes of all 3 brands are generally good. The old electro-forged Schwinns like the Varsity, Continental, Collegiate, and Suburban were not horrible bikes but they are far heavier than necessary, as in about 40 pounds. Also, Schwinn now makes a line of bikes sold at big box stores. I would avoid those. Ross made cheap gas pipe bikes, easy to spot because they lack lugs and have one piece steel cranksets. Similarly, there are a few Free Spirit models that were made in Austria by Puch that are good. The good ones have lugged construction.
Older French and British bikes like Peugeot, Motobecane, Gitane, and Raleigh might not be a good choice unless you have some basic mechanical skills or a willingness to learn them. Weird threads, cottered cranks, and plastic Simplex derailleurs on the lower end models can make working on them a little more challenging. But when they are properly serviced and adjusted they can be good bikes. By the late 1970s, Raleigh and some European brands began having their bikes made in Japan and eventually Taiwan. I feel that the quality of these later bikes is generally higher.
It never hurts to do a little research on the brand and model before you go look at a bike. The catalogs of many of the major brands are posted in various places on the internet. For example, Waterford Precision has catalogs from before Schwinn went bankrupt. Sheldon Brown’s site has a lot of the old Raleigh catalogs.
If you want some basis for determining a fair price, I find it useful to search eBay completed auctions. Ignore ongoing auctions since bikes often eventually sell for far less than a “buy it now” price, and some sellers tenaciously relist bikes at inflated prices. Also, in my opinion, bikes sold locally should sell for roughly two-thirds of completed sales on eBay because eBay auctions reach the worldwide market for used bikes, which includes well heeled collectors.
Notions abound concerning how properly to determine whether a bike fits, and rules of thumb have changed significantly over the years. Also, principles of bike fit that might work well for someone who’s racing on a drop bar road or cyclocross bike may have little applicability to someone looking for a city bike with swept back bars and an upright riding position. So for purposes of this article, I’m going to boil it down to a few basic criteria. First, is the bike sufficiently comfortable when you test ride it? The seller should be willing to raise or lower the saddle or stem to help you figure this out. Obviously you should be able to achieve sufficient leg extension without extending the seatpost above maximum height. Also notice whether you feel either too stretched out or too cramped as a result of the distance between the saddle and the handlebars. In addition, are you comfortable with how the bike steers and handles? Last, regardless of the above, there should be at least an inch of space between your crotch and the top bar when you straddle the bike. Here's a helpful video that shows what this might look like for you: