In the formats I've seen for writing a bibliography, the author is always put first, and then the title. Are there some bibliographies where the title is put before the author?
Craig knows of no "title-author" citation styles; neither do I.
There is a pragmatic reason not to put the title first: since titles may be long, titles are often permitted to be shortened on second and subsequent mention. To avoid the alphabetical ordering with title-author of the references to completely change from the full version to the short version, it would be necessary to forbid omission of words at the beginning of the title, which would be a very awkward constraint. With author-title, the "jumping around" of references is much smaller.
So besides the absence of evidence, I think we have reason to believe there are no such styles. Not that foolish construction of citation styles is unheard of, mind...
The person or group for which you're writing the bibliography probably has a required style, so you should go by that.
I'm familiar with APA and MLA, and they both put the author first. You need to have the first word in the bibliography consistent with the word you use in your in-text citations (or footnotes, if you're still doing those), and most styles that I'm aware of use the author's name in the citations.
If no author is available, things change a little, but it's pretty rare to find a truly reputable source of information for which you can't find an author or authors.
Chicago Style states that bibliographic list entries should be of the format:
Author last name, Author first name. Title. Location of press: Press name, Year Published
See here for more: http://www.isr.bucknell.edu/img/assets/6535/chicago.pdf
A quick scan through my bookshelf, and I can't find a single bibliography that puts the title first before the author, so I would suggest this is not usual. However, there may be some styles out there that allow it. I imagine that, as long as you're consistent, it should be okay, but I would probably stick to the more well known format above.