They don't slobber ! ( my favourite reason ! ( joking ! ) )
They look you in the eye when you speak to them.

There are thousands of them needing homes.

They are great with kids, and walk away instead of fighting. ( usually )

They're ADORABLE !!!! ( I had to say that. )

I would check out adopt-a-greyhound and http://www.greyhoundpets.org/chapters1.htm

I'll update as I think of more things.

P.S. I have a question, I was thinking of making a new thread for it, but as you have already captured the greyhound-lovers attention.

Q: What are the phisical abilities of a greyhound? I was thinking of teaching Jenny " sit up pretty" but I'm not sure if her hind legs could handle it.