A Flare for Fittings
There are two types of flares commonly associated with hard lines: 37-degree single flares and 45-degree double flares. We talked to the guys at Inline Tube to get the scoop on the differences (besides the obvious), and the proper applications of each.
Commonly referred to as A/N fittings (short for "Army/Navy"), 37-degree flares are primarily used only with aircraft-style fittings, and were never used in any production car. They are often seen incorporated on the fuel system of race cars and hot rods, and are usually used with braided steel lines. These fittings, however, are not recommended for automotive use because they are of the single flare variety and not strong enough.
The popularity of these fittings probably dates back to the days when you could purchase government surplus items from the local surplus store. These components are aircraft grade, but that's not necessarily better in automotive use. One of the main disadvantages is that the tube splits and cracks during the flaring process, and the crack will grow during use and vibrations, causing a leak.
Another problem is that any component (wheel cylinder, master cylinder, etc.) requires an adapter to work with A/N-style fittings, and these adapters aren't easy to find.
"Inverted flare" 45-degree fittings are used on every automotive application from the '30s to the present. The flared end is stronger and less likely to crack, and they also seal better than 37-degree fittings.
Swearing and Knuckle Busting Cure
Fuel and brake line fittings are made of brass, which is inherently soft. Line wrenches, sometimes called flare nut wrenches, are specially designed to grip as much surface area of a fitting as possible. This helps prevent rounding off the corners--a common result when using open ended wrenches. Contrary to popular practice, Vise-Grips are not the proper tool to work on line fittings! A good set of line wrenches from Craftsman costs less than $30, and should be considered mandatory. We've got two sets of line wrenches, so we can put a wrench on each side of a connection. Spread the investment over a birthday and Father's Day if you don't want to drop $60 all at once. It beats getting a tie!

Tale of the Tape
Never use Teflon tape to seal 45-degree flares. The flared end of the tube seats against the brass insert in the components and fittings, creating the seal. Teflon tape is used only on tapered thread components (pipe threads). A 45-degree fitting that is leaking is not leaking past the threads--it's leaking through the top of the fitting at the seat. To stop the leak, loosen the fitting and tighten it up again to reseat it. Repeat until the leak goes away. If the leak doesn't go away, the seat in the fittings is scarred or damaged, and needs to be replaced.
It's also important that you don't over-tighten the fittings. Simply snugging them up will cause the fittings to seat together. Over-tightening won't stop a leak.