Part of what an author needs to remember when asking this question is that there are only two different kinds of publishers as it relates to this question: Those who always accept unsolicited submissions and those who occasionally accept unsolicited submissions. This is important because persistence, content and luck are all required in order to publish a book, but for most authors nothing is more important that persistence. There is no publisher that will turn away an unsolicited manuscript if it is good enough.
The only caveat to that statement is that as authors we must remember that when we say good enough we are sometimes only thinking about content, where when they say good enough they mean good enough at earning a profit. As writers we have to learn the difference and keep working at understanding the economics that drive the business --frustrating as this may be.
The process is a simple but grueling one:
Every print publisher of any significant size will have a website and on their website you'll find a submission guide. This will give you usually very specific directions on how to submit your work and whether they accept unsolicited materials. Even if they say they don't accept unsolicited work, there is ALWAYS a way around that. That's enough for a whole other question though...
While I stand by my statement that, "There is no publisher that will turn away an unsolicited manuscript if it is good enough," there are imprints and brands for a reason. Readers put a lot of stock in the reputation of a publisher and so publishers tend to stick to one content area and do it well. Larger publishing companies usually segregate their different imprints and brands based on genre just like film production companies do. If you want to submit to every publisher in the world, go for it and be bold! But save yourself some time and money by choosing the best fits first.
Research what agents actually do. Try talk to some of them or listen to interviews with literary agents. Essentially, if you're submitting unsolicited manuscripts you will be doing all of those tasks on your own. Don't underestimate how much a good agent actually does. It's one thing to choose to accept these responsibilities out of necessity, but an entirely different matter to blow off the industry's accepted conventions without having a clue. Understand self-representation and the pros and cons --there's a lot more to it than just a bigger cut of the profits.
The arts are incredibly competitive and with the modern changes to the writing industry this is increasingly the case. There is a fine balance between doubt and over-confidence and if you want to succeed as a writer you will need them both daily. Always doubt that your work is done. If you think you're finished, look again, there is always something you can do to improve. Likewise, after you've given due diligence, believe in your product and represent it and sell it like it is made of gold and radiates a glowing aura beside a pile of scraps. Balancing this tension is crucial to approaching traditional publishing with the appropriate attitude.
The process of getting published can take years. I feel disrespectful even trying to answer this question in brief, but there are a lot of us out there, and it is good to help one another. If I could boil it down to one thought I would say: Always be refining and always be submitting. As long as you keep doing both of those things you're chances of publication will typically be increasing.