I have an illustrator text in Myriad Pro light 8 pt that I need to output to a png or gif. The quality degrades tremendously.
What is the best practice to get a good quality screen output on thin and small fonts?
At that size, for png or gif, I'd strongly suggest a different font. Such as what is known as a "pixel font". These are designed to not use anti-aliasing and appear legible at very small sizes.
One great place to get pixel fonts is FontsForFlash.com
If for any reason Scott's answer isn't an option*, one option of last resort for Illustrator font rendering nightmares is to take the two ways Illustrator has of rendering fonts, and find the best blend between them.
On Illustrator CS5 and above, save one 24bit png with Save for web with "Type optimized" selected (under the tabs on the right), one with "Art optimized" selected, then place the raster images with the "Type optimized" on top perfectly aligned over the "art optimized" image and adjust the opacity of the top image until you find the best balance between the two. "Type optimized" makes type stronger (and sometimes, unpleastantly blocky), "Art optimized" lighter (and sometimes, unpleasantly faint or fuzzy), and sometimes the best balance is somewhere between. You'll see as you adjust the opacity slider that the only thing changing is the aliasing of the edges.
On Illustrator CS4 or before, the "Type optimized" option doesn't exist, but the default preview rendering is very similar and often better for text than "Save for web". You can take and crop a screenshot to use instead of the "Type optimized" image, and use a "Save for web" 24bit png for the "Art optimized" layer, and then look for a balance point that works as above.
This can be a useful method for damage limitation in awkward cases - but whereever possible, it's almost always better to try to find and use a font that is designed for whatever awkward case you have (like those Scott suggests), or, to question and address the reasons why the awkward case exists in the first place (is there really no alternative to 8pt?). Don't be surprised if even the best balance of strong against light edges still doesn't look good enough.
*If anyone is saying that for branding or consistency reasons it needs to be Myriad, reason with them! Show them how at that size, Myriad barely looks like Myriad