This is a compilation of many of the different audio solutions available. It is not exhaustive. If you don't find what you want, search for it.
Please do not post questions in this thread looking for a solution that is not listed. Use other threads for that.
Please do post other good known audio solutions in this thread. I will try to incorporate any posted solutions into the list. Otherwise, users can read the thread for any other solutions.
ALC665 + VIA - Read this
ALC8xx - Use this Guide. General purpose audio guide for AppleAzaliaAudio.kext on many different audio chipsets. Appendix helps you locate your vendor and device ids for your two audio chipsets.
ALC 850 - Use this Guide
ALC 882 - If running the new 8.8.1 kernel, multichannel out and audio in using a Natit clone method here
ALC 883 - If running the new 8.8.1 kernel, multichannel out and audio in using a Natit clone method here
ALC 888 - If running the new 8.8.1 kernel, multichannel out and audio in using a Natit clone method here
SiS 7012 - Read this and this.
Soundmax - Review these: Guide 1, Guide 2, Guide 3. Note: Users with Soundmax 1981HD and 1986 have been successful using the ALC8xx method. Be sure to read the Appendix to the guide.
USB Soundsticks - USB Soundblaster and others. Read this and see below.
Other projectsUSB Soundsticks - very inexpensive USB sticks can be purchased for less than $10(US) to provide multichannel-sound out and microphone-sound in. One place to find these is on the eBay site by searching for "usb 5.1 audio". A higher quality device is the "Turtle Beach Audio Advantage" available in stores for about $35(US). All of these devices work very well when you have no other sound-out or sound-in solutions.
Audio MIDI Setup - use this utility found in the Utilities folder to cofigure your input and ouput ports