Are you using a new theme by any chance? The why could be how the theme is handling quotes. If you're using a theme you've used before that wasn't showing the slashes, I'm not really sure why they'd appear.
You can try a few things. Use single quotes instead of double. My guess is the same thing will be happen, but it's easy enough to try.
Escape the quotes by adding one slash in front:
It could be an issue in your database. You might have set it up with the wrong encoding. Here's how to fix. If it's a brand new installation with no real data you may want to just set up a new database with the encoding set to utf-8.
<a href=/"http://nyblogs.net/activity//"><img src="/http://nyblogs.net/files/2010/05/nysample.jpg/"></a>
I think the issue may be the database one. That was happening to me once and I think that was the issue.