Greetings,
I started a genealogy blog three months ago. I've noticed two blogs beginning to republish excerpts of my material, however they say the name of my blog and have a link back to my site.(Topics: Genealogy, Dogs)
So I figured this was a good thing because they could send me new readers.But now I've read through all the Google quality guidelines and I'm wondering:
1. Will Google get mixed up and start sending readers to the other blog instead of me?
2. Will Google consider it duplicate content and maybe close down my site instead of the other one?

It's spammy websites. Report the blog if they're on blogger. They just want to make money with YOUR content.

Plus: content duplication leads to more storage, and that depletes the Earth in the end.

The ones who republish an excerpt with a link back to your blog are usually hoping to get trackback links from your blog. In my experience they delete the excerpt after a while and replace it with other content, which you don't want your blog to be linking to.

Make sure your blog doesn't give them the trackbacks. Either turn off trackbacks, or delete the spammy ones manually.

Don't worry about Google. They have explicitly said that there's no risk of penalty from duplicated content which includes a link back to its source.