(Many thanks to Eric Shea for substantial contributions to these answers.)
How do I improve the braking on my 914?
Many first-time 914 owners are put off by the brakes, often because they have no experience with brakes that don't have a power brake servo. You just have to push a bit harder to overcome this. 914 brakes are also frequently neglected, and when they're not in tip-top shape, usually feel bad. Pistons freeze in the caliper, or the seals leak. Rebuilding the calipers is the only solution. Another common problem is the venting adjustment on the back calipers. The handbrake uses the rear calipers, and there's a manual adjustment that must be made to ensure the pads are 0.004" (0.1mm) away from the rotors with the handbrake off and no brake pressure is applied. This adjustment is frequently done incorrectly, leading to excessive pedal travel before the brakes bite. The Haynes manual describes the procedure, but incorrectly lists the adjustment range as 0.004-0.008". Try to get it as close to 0.004" as possible.
The system is also unusually difficult to bleed, sometimes requiring several tries to get a good pedal. This is usually caused by the misunderstood proportioning valve, which regulates pressure to the rear brakes to reduce the chance they'll lock before the fronts (which often leads to a spin). These valves rarely fail, yet a common "upgrade" is to replace them with a T-fitting, which (esp. with otherwise stock brakes), increases the percentage of the rear brake pressure, and can lead to premature rear brake lockup, which, as we said, can lead to a spin. A good method for bleeding the brakes is to bleed them twice, the second time after a day or so of spirited driving, to force the bubbles to the far ends of the system.
With fresh rubber flex hoses, rebuilt calipers, a new master cylinder, and good pads (in other words, like new stock brakes), the stock 914/4 brakes are more than adequate for even light track use. Keep this rule of thumb in mind: if you can lock your tires, the brakes are not the problem. Once you hit the traction limits of the tires, more brakes will not stop you any faster. With stock fenders, you'll hit the traction limit of nearly any tire that will fit with stock brakes.
If you cannot lock your (nearly stock-sized) tires, then you need rebuild or replace part of the system with stock parts.
What about the 19mm master cylinder upgrade?
This is pretty much a "feel" issue. The ratio of master cylinder piston area to total caliper piston area determines the mechanical advantage you get in applying pressure to the brake pads. The smaller the master cylinder piston (or the larger the caliper pistons), the more "advantage" you have (more force on the pads for less force on the pedal). However, while you apply less force, you have to push the pedal farther to get the same amount of movement at the pad. With a larger master cylinder piston (or smaller caliper pistons), you have LESS advantage, so you have to push the pedal harder, but you don't have to push it as far. The pedal feels firmer, but you're actually getting less braking. Some people like the feel this gives, so the upgrade isn't entirely a bad thing. However, many people make the upgrade because they think they're actually improving their brakes, when they're actually making them worse, just improving the feel.
What about braided stainless flex hoses?
These are commonly available, and people like them because they give better feel. Or so they think. The actual feel difference between fresh rubber hoses and braided lines is actually pretty small, and the improvement people note is usually wishful thinking, or they're replacing tired rubber lines with fresh stainless lines. The danger with stainless lines is that they require more maintenance and attention than rubber lines. Stainless lines are a braided covering over a Teflon hose. The braid is usually exposed, and gets dirty. This dirt works itself into the braid and begins chafing the relatively fragile Teflon hose underneath. This most often happens at the ends of the hose, near or under the crimped-on fittings. Given enough time, the Teflon hose will fail, usually with no warning. The result is a brake pedal that goes straight to the floor. If a front line fails, it also means nearly zero stopping power.
Rubber lines also fail over time, usually by swelling internally or cracking externally. This deterioration is slow, however, and there is lots of warning in the form of bad pedal feel and reduced braking, or obvious cracks in the hose. This process can often exist for months, so you have ample warning and time to get the car home and replace the brake hoses.
Stainless hoses are fine for racing use, as racecars are little used and frequently inspected. For a daily driven car, however, you're unlikely to inspect your brake lines nearly often enough, and the failure modes for stainless lines are hard to detect in advance.
Don't bigger calipers help?
Bigger calipers change the master cylinder to caliper piston ratio, providing more braking force at the caliper for a given pedal force. However, as noted elsewhere, many people consider fitting 19mm master cylinder to improve the braking feel, and this does exactly the opposite. Fitting BOTH bigger calipers and a bigger master cylinder does little more than cost you money with no improvement in braking at all, as you end up changing the ratio relatively little. Replacing a 19mm master cylinder with a stock-sized 17mm master cylinder will do exactly the same thing as fitting bigger front calipers alone.
Judging strictly by feel is not the best way to engineer a braking system. Fitting only bigger front calipers will improve braking at the front wheels, but you may now lock your front wheels long before the rears, potentially reducing overall braking. The 914 is mid-engined, not front-engined, and has a low center of gravity, so it does not require a brake balance that's heavily adjusted to the front, as many front-engined cars do. You have four tires, you might as well use all of them to slow the car.
Still other people like to replace the proportioning valve with a T, and often like the improved feel this gives (since you're now shifting the brake balance to the rear). However, you're risking locking the rears before the fronts, which lead to unstability under braking (try yanking on the handbrake sometime. Now do it while turning). The T people are also doing directly the opposite of what the big front caliper people are doing. Both are moving the brake balance, which is only useful if the Porsche engineers got it wrong, and placed it too far front or too far rear.
So, when DO I need to make brake upgrades?
Brakes turn speed into heat, and the amount of heat varies with the mass and speed of the car. Heat has to be gotten rid of, and more heat requires more rotor area to disperse this heat without getting so hot that the brakes "fade". Pad material is also a major factor in dealing with heat. Brake fluid can also be a large factor, as inferior fluid will boil at lower tempertures, which also causes fade.
If you substantially increase the weight of the car (like fit a V8), you're a candidate for a brake upgrade. If you substantially increase the power, you're also a candidate. Heavy track use may also force an upgrade, as the brakes frequently don't have enough time to cool off between heavy applications.
On the street, even with some weight and power increases, a brake upgrade may not be required. The key to finding out if you need to do this is careful testing after the weight or power increase. Brade fade usually takes a lot of effort to induce, and if you can make it happen, then you need to reengineer your brakes.
Start with pads, using pads specifically designed for track use. Follow that with brake fluid specifically designed for track use with a high boiling point. If that's still not enough, progress to vented brake rotors (911 parts are relatively easy to adapt), first at the front, then at the rear. Vented rotors nearly always require different calipers (wider, to accept the wider rotor).
The other time you may need a brake upgrade is when you fit flares and wider tires. In this case, what may happen is that you find you can't lock the tires with the stock brakes. In this case, you actually need to re-engineer the ratio of master cylinder to brake caliper pistons, as you need more force at the caliper for the maximum force your leg can deliver to the pedal. A smaller master cylinder, or larger caliper pistons (the total area is important, so four small pistons per caliper may be much larger than two large pistons per caliper) will be what you need. You may also need vented rotors, as you'll be generating a lot more braking force, and thus more heat, so you need bigger rotors to eliminate that heat.
Any time you're doing this, you're re-enginering a system. Just fitting random parts is not likely to improve things without hurting some other aspect of the system. Be careful.
If you'd like to pore over all of the physical details, here's a link to a series of papers online on the subject: Stoptech White Papers
What about the 911 handbrake setup?
The 914 rear calipers provide the handbrake setup. On the 911, the handbrake is provided independently of the rear calipers by fitting a small drum brake in the "hat" of the rear rotors. The 911 handbrake setup CAN be fitted to the 914 trailing arms, but it's not a straightforward bolt-on procedure. If you're seriously reengineering your brakes and want to use rear calipers that don't have a handbrake mechanism, the 911 handbrake setup is an option.
Here is a thread that covers the conversion process.