Traditional big publishers have offered readers the implicit bargain; "We've put our experience and money behind this book, so you can confidently buy it." We can all offer counter-examples, but we can't deny that this unspoken support will make most of us more likely to buy a book labeled, Tor, Ace, Signet, Ballentine, etc. over some logo that we've never seen before. For bookstore buyers, it is even more of an issue. Many small imprints never get stocked on the shelves.
When the SFWA, the MWA and the RWA all spoke against the Harlequin project they explicitly validated the idea that books from big publishers were better than those that are self-published. Unread and unjudged, books were banned from consideration for association awards. Chuckle at that. Author organizations banning books.
So what is a self-publisher to do against this entrenched (and understandable) bias. If you've got a good book, you have to do without the advantage of familiar logos on the spines of books. You have to have sold the book before the reader discovers it as one of many on the shelf. Your book has to have been recommended by a friend, a good book review, or by having won an award.
There are different kinds of awards. In the science fiction world, the big names are the Hugos and the Nebulas. Both of these are popular awards. Books are nominated throughout the year and then a group votes on the finalists. The Hugos are voted on by people with a membership to the World Science Fiction Convention of that year. The Nebulas are voted on by members of the Science Fiction Writers of America. In each case there are thousands of potential voters, with a smaller number actually voting. I class these as popular awards because to have a chance at winning, your book has to have been read by a large fraction of the voting population. A small press has little chance to make a big splash here, because the award only happens after the book has already sold well.
There are also juried awards. In these cases, a small group, sometimes as large as a dozen and frequently smaller, reads nominated books from a pool and votes among themselves. While the books may be nominated by a large group, the small number of judges allow a small press or an individual author to make sure that the judges have at least had the opportunity to read the book. This is a wonderful opportunity for a well written, but otherwise invisible book to be recognized.
Juried awards are much more common than popular awards, and their prestige varies by the sponsoring organization and how long they've been at it. I won't even attempt to list them, because there are so many. A couple of lists to get started are here and here. Search the lists and find all that your book is technically eligible for and make sure the judges have copies. I've been lucky to have won a couple of awards for my books and it makes it much easier to confidently introduce yourself and your work when you know that total strangers have linked the reputation of their awards to your books.
There is still a third class of awards that you should know about. Certain organizations essentially sell awards. Read their website and notice these common features: There is an up-front charge to enter your book (in addition to copies of the book itself). There are so many categories and classifications that hundreds of people can win. The judges are not listed, or in one case I know, there is just one judge to make the decision for hundreds of awards over the course of a few days. And if you win or are a finalist, the organization will sell you stickers to mark the covers of your books. I'm sorry to say that I entered one of those contests before I realized what was going on. Never again.