The primary purpose of an aftermarket turbo is to increase the performance over the stock unit. This can be accomplished by choosing a turbo with better spool, more flow, or a combination suited to the end user's needs.

What is some good background turbo information?

howstuffworks.com's turbo walkthrough
Wikipedia on turbos

Common Terms:
Boost threshold- the lowest RPM at which a turbo will generate positive manifold pressure at maximum engine load.
Turbo lag- the time between hitting the throttle and the turbo providing full boost.

Recommended Reading:
Maximum Boost by Corky Bell is considered by many to be THE publication for turbocharger information.

What is the best turbo? There is no best turbo. Generally speaking, aftermarket turbos fall into these generic categories:
a. Turbos with a little more top end power
b. Turbos with a lot more top end power
c. Quicker spooling turbos

What do all the names and numbers of turbos mean? This link sorts many of them out nicely.

What supporting upgrades are required for aftermarket turbos? At a minimum, aftermarket turbos require a fuel pump, injectors, and engine management for safe operation.

What is my stock turbo?

2002-2008 WRX TD04-13T
2004-2005 STI VF-39
2006-2007 STI VF-43
2008 STI VF-48

Is there a turbo upgrade that does not require other upgrades? Yes. A ported and polished (P&P) stock turbo is an easy upgrade over the stock unit. Though there are many turbos that may be used for short periods of time with a boost controller, it is generally unwise to bolt on an aftermarket turbo with a boost controller.

What is the best turbo with a little more top end? The most widely used turbos meeting this criteria are the VF30/VF34 and the 16G.

What is the best turbo with a lot more top end? The most widely used turbos meeting this criteria are the VF22, 18G, 20G, FP Green and it's clones.

What is the best turbo with quicker spool? The most widely used turbo meeting this criteria is a P&P stock turbo.

What makes a good autocross type event turbo? The big thing to look for in a good performer for autocross use would be quick spool and more than stock flow. The TD04, TD05-16G, VF34, VF22, VF39, 16G, and 18G can all be considered good autocross turbos, but their particular suitability depends on the type of events where the car is generally run. During the consultation with your Vendor, discuss in depth the course length, speeds seen, gears used, and other local venue particulars to assist in determining what best suits your needs. A word of caution....before modifying or changing your turbo, be aware that this will have an effect on what class your vehicle can legally run.

Is there a way to compare Turbo A against Turbo B? Yes and no. This link, this link, and this link show comparative lists of most of the major aftermarket turbos. These listings should NOT be the sole source of turbo upgrade advice though. It should be used as a general indication as to the performance level of various turbos. Matching turbos to your specific needs is where advice from Vendors and tuners comes into play. You will not be happy with the perfect tune on the wrong turbo and likewise, you will not be happy with a poor tune on the perfect turbo.

What is the best way to compare Turbo A against Turbo B? Careful interpretation of a particular turbo's compression map will give you the best determination as to what will best suit your needs. One reason for this is that Turbo A will flow XXX CFM for a 2.0 liter, and will flow YYY CFM for a 2.5 liter. Displacement can change a "perfect WRX turbo" into one that is less desirable for someone running 2.2, 2.5, or other displacement. Sadly, some turbo manufacturers do not release compressor maps to the public or even their retailers. This means that in the end, the user must consult available compressor maps as well as seek the advice of Vendors and tuning specialists for "best" suitability.

How do I interpret turbo compressor maps? General guides with examples can be found on this link, this link, this link, this link, this link, and this link.

Where do I find turbo compressor maps?
Website 1
Website 2
Website 3
Garrett maps
Garrett maps (via their .pdf catalog)
Other turbo data

Should I upgrade my wastegate & what advantages would it give? There are a couple of different upgrades for wastegates that will help to solve different problems. Upgrading the wastegate actuator to a higher rated version will allow a higher boost threshold. For example, if a turbo has an 11 PSI actuator, with a good boost controller it can normally be adjusted to about 19-20 PSI, but no lower than 11 PSI. A 15 PSI actuator can easily be adjusted to 23-24 PSI, but again, no lower than its stated static pressure. There are also race actuators available for 19, 24, and 29 PSI. The inverse of this problem/upgrade scenario is a turbo that allows boost to rise beyond its target point. In some cases, very free flowing exhausts combined with the right supporting mods and a hot tune can cause turbos to not be able to vent through the wastegate properly. A condition that allows the car to continue to build boost beyond its target, even with the wastegate flapper in its full open position is known as "boost creep". Boost creep can be alleviated by several methods; a turbine clip can allow slightly more air to vent through the turbine blades, retuning the car to a slightly richer mix can help in some cases, and in some cases the standard size wastegate flapper can be removed, the hole enlarged, and a larger, more efficient flapper installed in its place. In some cases this will require a retune, especially if boost control is handled by the computer. The larger flapper, in most cases, will help eliminate boost creep events; however, on some of the IHI turbos, this can cause additional work to need to be performed. The IHI's are more sensitive, so on some of these turbos, the restrictor "pill" in the wastegate actuator vacuum line will need to be changed to a different size to accommodate the changed actuator duty cycle brought on by the larger flapper.

When do I go with an external wastegate? External wastegates and when to use them have become some of the most commonly asked questions in the turbo business over the past year. External wastegates move the wastegate vent from inside the turbine housing of the turbo to a remote location, fed from the same tube (or uppipe) as the turbine inlet for the turbo. There are several advantages as well as drawbacks to this setup. The first, and in many cases, the drawback that discourages most Subaru owners, is the cost. Not only are you adding expense to your turbo upgrade through the wastegate assembly, (normally starting at about $200) but there is also the additional cost of custom piping. Due to the design of the Subaru, it is more difficult than many vehicles to install/fabricate piping for the external wastegate units. This normally adds another $100-$200 in labor costs from a good exhaust shop. There are companies now offering custom uppipes with flanges for the use of external wastegates, however, due to differences in input flange on different wastegates, these are not universal. The biggest advantage to the external gate setup is boost control stability. In very high horsepower cars it becomes necessary to have a large enough port for wastegate venting that it is simply impractical to attempt the use of an internal setup. The larger external units will be able to hold the boost pressure more stable, and require very little actuation to vent fully and stop boost increase. It is this benefit that many times causes a vehicle with an external wastegate to produce additional power over an internally gated turbo, and is how the external has become known to produce more total power. Normally with proper turbo design and proper tuning, externals are not actually needed until power ranges rise into the 600 or greater HP range on a single turbo setup, and 900 or greater HP on twin turbos.

Are there any downsides to turbos? There have not been significant amounts of problems with turbos. The main downside to turbos in general is uneducated usage. Careful planning, purchasing, supporting modifications, and tuning should allow the end user long and happy usage. Too often, many users take shortcuts, exhibit poor planning, or disregard necessary precautions and end up with disappointing failures. Another downside is poor selection which leaves the user disappointed as the new turbo's characteristics don't meet their expectations. The two main disappointments are:
a. Not enough power
b. Incorrect spool characteristics for autocross and daily drivers

Which manufacturer is best? This topic is highly debated. There are just too many factors to consider. The main category breakdowns are:
a. Price
b. Performance characteristics
c. Warranty
d. Compatibility with end user's desires
e. Bolt on or custom fabrication installation

Who manufactures turbos?
APS
AVO
Blouch
Deadbolt Enterprises
Element Tuning
Forced Performance
Garrett
IHI
Mitsubishi
Power Enterprise
Slowboy Racing
turbochargers.com
Turbonetics

What turbo construction method is best? There is no irrefutable evidence that one construction method is better than the other. The real difference in turbo construction is the bearings. There are two main types: floating bearings and ball bearings. Ball bearing turbos were designed for increased reliability and decreased lag. Though both of these elements are true, neither advantage is especially prevalent, so the construction method should not be the main consideration when choosing an aftermarket turbo.

What is a twin-scroll turbo? Generally speaking, it is a turbo with a divided turbo inlet to isolate the pulses coming from each exhaust port to maintain more of the pulse energy from each cylinder all the way down to the turbine wheel. A twin scroll setup will respond faster and produce boost quicker than a equally CFM sized regular turbo. Twin scroll setups are generally costlier and require more components than the average turbo ugrade to work efficiently though due to their requiring a true twin scroll header to operate correctly. Fitting a regular header to a twin scroll turbo basically negates the pros of this type of turbo.

So a twin-scroll turbo spools faster? When properly set-up and compared to an equal CFM regular turbo, yes. However there are many regular turbos that will outspool twin-scroll units. Generally speaking, buy a turbo based on HP/CFM and consider a twin-scroll if there is one that fits your goals and you are looking for decreased spool. Never buy a twin-scroll for the sake of saying you have a twin-scroll. Play into the benefits of a properly thought out twin-scroll set-up, not the marketing hype.

What is a rotated mount turbo? Any turbo that's physical size prevents mounting in the stock location. They also generally have larger than an OEM inlet size which necessitates TGV deletes and a larger turbo inlet pipe. They also require custom exhaust components and generally use an external wastegate set-up.

How can I decrease turbo lag? There are a number of steps that you can perform to decrease the lag:
a. A silicone Y-pipe IC hose can decrease lag
b. An aftermarket intercooler with decreased pressure drop can decrease lag, though its physical design may negate the benefit
c. An aftermarket uppipe can decrease lag
d. Port and polish turbo services can decrease lag
e. Tuning. Through the tuning of EGTs, wastegate duty cycles, and gains, spool can be accelerated. Properly tuned cars create full boost ~500 rpm sooner through these techniques.
f. Large diameter downpipes and exhaust decrease lag. If the downpipe is catless, lag with be further reduced over a high flow cat model. You also want the cat to be as far from the turbo as possible to promote quick spool.