The only reason I've been able to sell novels on my own is because I first sold novels with an agent, and still, in fact, have an agent. I did sell two novels when I was between agents, but only because the publisher had already bought books from me through an agent.
Two of teh other books I sold on my own nevertheless went through my agent after I made the initial deal, and which happened at all only because an editor I'd worked with had an idea he thought I could handle, and contacted me about it. I listened, said it was something I'd love to do, and to send my agent a contract. She hammered out the details.
The fifth book was a true anomaly. I won't go into intricate details, but I had an idea in a genre my agent had no experience at all in, so i asked her if she would mind if I contacted an editor I knew on my own.
It got pretty complicated after that because, well, for a lot of reasons, but I ended up selling that book completely on my own.
At any rate, you can sell a book directly to many publishers, if you have a book that's good enough, and if you have the experience to know how to get that book in front of a good acquisition editor. This is easy with some publishers, very difficult at others.
I know a writer who manage to get a deal with a big five publisher all on his own, and with no prior publishing experience, but a whole chain of events had to happen, none of which were under his control. Something like this is extremely rare.
But with small to mid-size publishers, you really don't need an agent to get a book deal. You do need a very good book, and a lot of patience, but it can, and is, done fairly often.