In the United States (the jurisdiction where Stack Exchange is located), you may make fair use of copyrighted material. The definition of fair use is fairly complex and mostly determined by jurisprudence rather than statue; the law stipulates that
the fair use of a copyrighted work, including such use by reproduction in copies or phonorecords or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include:
- the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
- the nature of the copyrighted work;
- the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
- the effect of the use upon the potential market for or value of the copyrighted work.
If your blog post is reviewing a work, then it falls under the heading of criticism or comment, and the inclusion of short extracts (such as a few movie stills) to illustrate the blog post is likely to be fine, given its low score on criteria #1 (the blog is not directly for profit), #3 (you are only posting a very short extract) and #4 (your extracts are not a substitute for the copyrighted work).
Of course, not being a lawyer, I cannot give you legal advice, so whatever you publish is your responsibility and not mine.