Forgive my ignorance, but which is more Google or search engine
friendly, www.seespotrun.com or www.see_spot_run.com?

Personally, I don't like the underscores. Reminds me of something a 13
yr old would do to 'spice up' and make their site different. Generally
most sites don't use them, try to stay away from them. Ask yourself
"How often do I see a site with underscores on Google?" - hardly ever

If your domain name contains a combination of names that alot of
people are searching for, then it would be better to separate the
names with a dash (not an underscore). When you separate words in a
domain name with a dash, the search engines 'see' the individual
words, and will give the domain a little more weight than if the words
were not separated with a dash. If getting a good ranking with the
search engines is important to you, then making sure your site is full
of lots of good, relevant content is much more important than the
choice of domain name. There is really a huge science behind all of
this. Type 'Search Engine Optimization' into a search engine and
you'll see what I mean. Hope this helps...

I agree, I've never been to an 'honorable' site that had underscores.  That is rare.

Hello

Actually underscores are invalid characters for a domain name.  They
don't exist.  The only valid characters are letters, numbers, dashes,
and the dot.
If you see underscores after the slash such as
website.com/this_page.html - that's a URL, link, sub-directory, or
page but not part of the domain name.  The domain ends before the
first slash.

The bigger question on selecting domain names is how intuitive it is
and how easy to say and type.  It's much simpler to tell someone to go
to "seespotrun.com" then saying "go to see dash spot dash run.com"

This is a technique that has come and gone. Much better to get  one
that is EZ to remember or say over the phone.

For interesting articles on SEO, I would suggest you visit:
http://www.websitetrafficbuilders.com