Google and Yahoo! are comptetitors on every front.  There’s Google Maps/Yahoo! maps, Google Video (the ubiquitous YouTube)/Yahoo! Video, and GMail/Yahoo! Mail.  As far as the last two go, I have played with both and I have to say I think Google is the clear winner here.  I’m sorry, Yahoo!, but your ads are so obtrusive.  You might have a fancier interface (in the Beta testing mode) but GMail is just so much simpler and cleaner.  Yes, drag and drop and tabbed e-mail messaging is great, but your ads are a HUGE eyesore.