First to Worst:
ENIG: What to watch for - Excessively thick gold or thin Nickel.  Nickel should be 130uin to 180uinch.  As there is some nickel loss during the Gold process, if the nominal of 177uin is applied, I would expect to see 160 - 170 uinch post immersion gold.  thick nickel is not a problem, but is a waste of metal, below 110 uinch and there are concerns of excessive loss during the immersion gold process.
Gold should be 1.5uinch to 4.9uinch.  
Gold: 5 uinch and above is a strong indicator that you will see black pad.  Below 1.5unich will not provide adequate sealing of the nickel.

IAg (Immersion Silver): if you are using a board stacker, it likes to smear.  Also, MUST wear gloves as well as salts impact its processibility relatively quickly once you start heat (reflow) cycles.  An investment in Silver Saver paper is in order.  Has only fair shelf-life (3-6 months), although I have used boards that were 2 years old without issue if they were sealed in bags with saver paper.

HASL (Either variety): tends to have pools an uneven thickness.  Not horrible, but not friendly with CSPs and 0201 and smaller.  Also, pay careful attention to stencil thickness as you already have roughly 1 mil of solder in the connection to start.  I recommend going 1-2 mils thinner on your stencils if using this if you are most familiar with a plated finish.

Immersion tin: All the bad points of IAg and few of the good points.  It is cheap, but oxidizes rapidly.  Like the IAg, the silver saver does help.

ENEPIG: Trendy, but not easy to obtain and has a plethora of concerns.

OSP: Tends to be 1 (reflow) and done.  Short shelf life, variation in OSP thickness, not suitable for BGAs.  Also, if doing any sort of post processing, it is best to pre-tin these features.  I worked with the stencil house I mentioned in previous posts (Metal Etch Services) to develop some of these tips and tricks to aid in making this finish more user friendly.  Does not work well with RMA based solders.  ORMs and ORHs work best to cut through the OSP and etch the copper enough to get good connections. 

That pretty sell sums it up.