In my research of what to do to record samples for my own mixes, I stumbled upon this interesting guide. I've changed some of the product lists so it doesn't interfere with this forum's rules, as I only want to pass along some info that has helped me:
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What is a "VST"?

VST is an acronym for Virtual Studio Technology. The term is being used here to describe software instruments, such as drums.

OK, what is a "Software Instrument"?

A "software instrument" is basically a synthesizer or sampler that runs on a Mac or PC and responds to MIDI. Consider for a second the internals of a drum module. They include a specialized computer, a sound generator/sampler and a method for converting analog input signals to MIDI information which are then used to trigger the onboard sounds. Almost every module includes a physical MIDI output so that the same MIDI information used to trigger the onboard sounds can be sent to other devices.

So, a "Software Instrument" can also be thought of as the sound generator portion of a module running on a MAC/PC, instituted as a plugin standardized by an existing specification (VST, RTAS, AU). This is so that they can be loaded into any comprehensive audio/MIDI application (hosts, DAW, sequencer) that conforms to a standard.

Manufacturers of "Software Instruments" (which I will now call "VST" once again for the remainder of the document) will sometimes also provide a host application for running their plugin in "stand-alone" mode, making it simple to launch and play.

What is needed to play a "VST" in real-time?

For starters, you will need a computer. It generally does not need to have the fastest CPU. In fact, computers that are now several years old can easily handle VSTs in real-time. For drum VSTs, lots of memory is usually needed. 2 GB RAM or more is best for having no problem running the associated software and O.S. comfortably, without cutting corners.

Next priority is computer audio/MIDI hardware. The "sound cards" that come with computers are generally not geared enough toward professional audio to perform to your satisfaction. They may sound OK, but the speed at which they can send the sound to your ear is critical (the delay of sound is referred to as "latency", discussed later.). To that end, you want something marketed toward the pro/semi-pro audio mixing/recording market.

One of the identifying characteristics of knowing if such a device is geared toward that market is when "ASIO Drivers" are included. In theory, any device that comes with ASIO drivers will do the trick (though not all such devices are created equal). A computer audio device with a MIDI input, line stereo output and a headphone output is all you need, but you'll also find many devices that come with multiple outputs (these are also fine) and many other features.

You can also separate the audio and MIDI hardware into two devices (a dedicated MIDI input), however, most pro audio hardware package include MIDI I/O and two devices are generally not necessary, depending on your purchase.

Last thing to note regarding audio hardware is how the hardware will interface with the computer. 3 main choices are USB, Firewire or PCI (PCIMIA/cardbus if using a laptop). For the best "real-time" audio performance, look for PCI or Firewire.

Lastly, you will need a drum module with a MIDI Output. You probably already have one. Almost all drum modules have a MIDI output and you will need to hook up a MIDI cable from your module's MIDI Output to the MIDI input you've added to the computer above.

There are also a few drum devices that are only for sending MIDI and do not include their own onboard sounds. In a larger sense, these are called "MIDI Controllers", but in drumming, they are more often referred to as "Trigger-To-MIDI Interfaces".

The Physical Hookup:

As already stated, you will connect the MIDI Output of your drum module to the MIDI Input on your computer's Audio/MIDI hardware. At a minimum, you will plug headphones into the headphone output of your computer's Audio/MIDI hardware. If you also need to send audio to other amplified sources, use the audio line-outs of your computer's Audio/MIDI hardware (same as you would on a drum module).

If you have a VDrum module with a Mix-In, you may also try sending the line stereo outs from the computer's audio hardware to the module's Mix-In, then allowing you to use your module's headphone amp.

Using the VST:

If you want to just load up and jam, use the "Stand-alone" feature of your chosen software if available. These start up to automatically receive the MIDI data and send the audio output with minimal configuration. Technically, the "plugin" is still being used, but it has been wrapped by a lightweight host to facilitate easy usage.

If you want to record, or if your chosen software does not include a "stand-alone" mode, you will need "host" software. Host software refers to any package that provdes a MIDI and Audio environment and can load plugins under a compatible standard (VST, RTAS, AU). There is a bit of a learning curve here, and it differs based on the host software you load. The best way to start is to consult your software's documentation, usually listed under a heading like "Using Virtual Instruments", "Software Instrument" or "VSTi" (VSTi is the proper technical term for a VST that is an instrument vs. one that is an effect unit).

About Latency:

Latency is the amount of time it takes from when you hit the drum pad until you hear the sound. Every device has latency, including drum modules themselves. While black-box modules do have the fastest specs for latency, it is a myth that the latency of a VST solution is too slow. If you are experiencing noticeable latency with your VST and you have a pro/semi-pro audio device in your computer, there are adjustments that can be made within the driver control panel or host software to "speed things up". Namely, you decrease the value for the "Sample Buffer". A value lower than 256 is generally acceptable. 128 or 64 is possible on many systems. If the setting is so low that your computer audio cannot keep up, you will hear "pops and clicks" in the audio and you should increase the buffer setting to the next highest value or examine the VST's own configuration for increasing efficiency. All that is usually needed is to find the sweet spot on your system to where you do not feel any latency while you play and you do not hear any pops.

Possible Additional Gear to Consider:

As with anything, the laws of GAS apply here. And there are plenty of things to add on. I think that one of the best add-ons is an inexpensive headphone amplifier. This is because the headphone outputs of many computer audio interfaces are not of such design as to push your headphones above the sound you make when you strike the kit.

Brands, Pros, Cons, etc:

That is enough of an overview to get started. Until you own the gear; the details, benefits and headaches will remain esoteric and distant text. As with any technology, people have different experiences. None can argue against the fact that VST drumming has evolved greatly in the past 4 years, in terms of easier setups, terrific sound and feel. There is still some ways to go to make it a turnkey solution. Its clearly here to stay as these drumming "VST" solutions plug into much larger computer audio/studio paradigms that have been going strong for decades.

Others should feel free to add to this thread with specific brand names, devices, benefits, drawbacks and detail.
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Brands/models

Audio/MIDI Hardware:
Echo Audio:

EMU audio:

Focusrite (Saffire):

M-Audio:

Mackie:

Presonus:

RME audio:

VST Drum Software:
fxpansion (BFD):

Ocean Way Drums:

Steven Slate Drums 3.0:

Toontrack (Superior Drummer, EZDrummer):

XLN Audio (Addictive Drums):

Drum Sample Expansion Libraries:
Platinum Samples (BFD Expansions)

Host Software (DAWS, Sequencer)
Apple (Logic, GarageBand):

Ableton (Live):

Cakewalk (Sonar):

Digidesign (ProTools):

Mackie (Traktion):

Reaper:

Steinberg (Cubase):

Modules/Trigger to MIDI Interfaces:
2Box DrumIt five

Alesis Trigger i/o

MegaDrum

Roland TMC-6

Yamaha dtxplorer/dtxpress/dtxtreme/dtx series