A Corvair has an advantage over a front engine car under braking. Since the weight bias is to the rear, the car is much less nose heavy under braking, so it makes use of all four tires when stopping. Early model Corvairs had adequate, though not spectacular, brakes and the rear weight bias helped the car use all four when braking. Late models used GM intermediate platform (Chevelle, Tempest, etc.) brakes which performed very well on the 1000 pound lighter Corvair. FCs use full size Chevy brakes and they too work quite well on the lighter Corvair trucks.
Corvair brakes still perform just as well as they did over 40 years ago. What's different are the tires. Many folks forget that in terms of actual stopping distance the only way to improve the performance of a car that can lock up the wheels is to get better tires. These tires then are capable of more torque which translates to more heat in the brakes.
Fortunately, all is not lost. There have been advances in brake technology over the years, and many of these advances work very well on Corvairs.
Many folks want to swap out the entire system for disc brakes. While discs are better than drums in many ways, many of the complaints can be solved by simply going through the existing brake system to get it to function the way it was intended. Even if you're running your Corvair in a stock class competition and can't change very much, the difference between so-so brakes and those in top shape is easily measured on a course.
Bear in mind all of these fluids are hydroscopic, which means they absorb water like a sponge, right through the rubber lines. This water reduces the boiling point of the fluid dramatically (that's the "wet" value). It's good practice to change the fluid once every year or two.
In many classes, you can swap Yenko parts onto your car, but you must keep the basic original system. This is not entirely a bad thing for an autocross/street car. Drum brakes are often lighter, and reducing unsprung weight in the suspension is a great help to handling. Finally, simply modifiying the stock system is less expensive than a complete swap. Modifications to consider:
For earlies, I checked to see if rear drums from a Datsun 240 - 280Z would work, but they don't fit. It is possible to change all four drums over to late model sizes by swapping a late front suspension and FC axles on the car, but be aware that the track will be wider so you'll likely need to trim the fenders or buy custom wheels.
Every new car you can buy today has at least front disc brakes. On many cars, they are too small to offer any real improvement over drums in terms of raw stopping power, but discs do offer the advantage of generally having less effect on the directional stability of the car under braking. A drum brake car will often dart because the brakes don't engage at exactly the same time. Disc brake cars usually don't have this problem because the pads constantly ride on the discs. Of course it's also possible to dramatically increase the fade resistance for repeated high speed stops by using larger disc rotors, since disc brakes cool much better.
There are several different kits out there to convert your Corvair to discs, both front and rear. Be aware that for SCCA E-Prod racing, you are limited to specific rotors and calipers. Check the rulebook for the most up to date info, I believe it was written as 11" non-vented rotors (a GM standard size) but that may have changed by now. Jeff Moore pointed out that the rules allow you to run the same rear brake as the front, so any rules affecting front brakes give you the same option for the rear. Bear in mind that 13" or sometimes even 14" wheels will not clear most of these disc conversions, so check before you buy.
Note: If you only change one pair of brakes to disc, be sure that you consider all the changes needed. Disc brakes use more line pressure than drums, so this may require you to use a disc/drum specific master cylinder, a proportioning valve, and a residual valve. See the Master Power brake site for more info.
Here's some general information that may be useful, gleaned from a variety of sources: