Can a web site quote another’s blog posting?
Yes. Short quotations will usually be fair use, not copyright infringement. The Copyright Act says that “fair use…for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright.” So if a user of your web site is commenting on or criticizing an item someone else has posted, then the site likely has a fair use right to post the quoted content.