I have a little digital organ that runs through software on my computer.
The midi keyboard is an M-Audio 4 octave keystation. I designed and made the desk.
The software I use is called Hauptwerk. A basic free edition of this is available at Hauptwerk.com. You have to connect a keyboard to load it. You need a computer with at least 2 gig ram, better with 4 or more gig. The software comes with a 2 manual English Cathedral organ. Obviously I can only play one manual at a time. There are quite a few other digital organs available free of charge. I also have a steam calliope, and a 2 manual harpsichord.
The better your speakers, the better the sound. If you have good quality head phones, it will sound very good, too, but I don’t like wearing them very much.
You may have to do some experimenting to get it set up properly; the main issue is that your computer and your keyboard have to talk to each other.
This is set-up is the simplest I can think of. But you can use Hauptwerk to set up a complete organ, if you are prepared to shell out money. You can buy manuals and a pedal board designed specifically for use with Hauptwerk. You can also set it up with touch-sensitive screens for stops. Then you can buy the digital capture of at least 150 pipe organs.
You can explore the possibilities at a number of web sites, for example http://www.midiworks.ca/