http://www.google.com/search?q=pegasuses&sourceid=navclient-ff&ie=UTF-8&rlz=1B3GGGL_en__205__205
No google, I sure as hell did not mean that.
Maybe it thought you wanted to search for something that uniquely belonged to Pegasus. 
I think they get those suggestions based on other search data or available search data, not on the dictionary. So if 99% of all similar searches are “pegasus’s” or 99% of all similar search results are “pegasus’s” (if it is spelled that way on a lot of pages), then they’ll suggest that.
Plus, it might be directing you to the possessive of “pegasus.”
Seeing as Pegasus was a unique creature, IIRC, there might be more call for the usage of the possessive rather than the plural.
Ah, a Buddy Holly fan.
Exactly. Pegasus’s is a real word used in twice as many web pages as the plural.
The reason the plural is hardly used is because there was only ONE Pegasus. So why would you you ever use the plural of it? The plural would be “flying horses”, not Pegasuses. Regardless, Google was offering you an alternative that would produce twice as many web pages as your word. I can’t see how that’s letting you down. :rolleyes:
besides, wouldn’t it be pegasi? 
What if I want to talk about the flying horse and the constellation? Huh, smart aleck?
Would that be a herd of pegasi or a flock of pegasi?
Well, if it’s any comfort at all to the O.P., Google has not let me down. You see, this thread set me aimlessly wondering which was the chain of petrol station that used to use Pegasus as a logo. (Mobil, apparently, in case anyone else now wonders).
However, Google did, admittedly, turn up a whole lot of hitherto unheard-of Pegasuses or Pegasi. Software! Theatres! Retirement Homes! Probably lions and tigers and bears, oh my, too, but I had a quick flash of sense and closed that window.
So many pegagsuses, who knew? 
And, NOW, you evil Gentle Robot, just when I thought I had done my trivia fix for today, I wonder why the heck Mobil people decided that Pegasus was bright red. (Yes I AM procrastinating and putting off doing some household stuff - is it so obvious?)
Huh! Damn you.
Oh, yes, and welcome to the Straight Dope.
Likely not. Pegasus is a Greek word, and Greek plurals don’t work like that.
I think Taber knows that and is referencing the octopus, octopi, octopod discussion (brawl?) from a few months ago. Proper Greek and Latin pluralizations are very important to some people.
I don’t see what’s wrong with it.