Lots of ways.
First, consider FSBOs. Some will have paid a flat fee so their property can be listed in the MLS, but most won't. Most FSBOs finally end up getting listed with a Realtor, so they will end up there eventually. But you may have a 30 day, 60 day, or greater head start on someone who's just scanning the MLS.
Second, tap into the world of houses that aren't listed, but may be for sale. There are dozens of different ways. Here are just a few:
If you're interested in a particular neighborhood, do what Realtors and investors do: Direct market. Send a letter to each person in the neighborhood or building along the lines of: "I (or my spouse and I) really like this neighborhood and would like to move here. Do you know anyone in the neighborhood who is thinking of selling their home?" I've heard of people who'll go door-to-door with the same message, and they come up with results. I've done it, and found properties that the owner planned on putting on the market in a month or two.
Look at properties for rent. Now, not all of them will be for sale. But, especially in today's market, many people are discouraged and figure they can't sell today, so they'll have to rent out the property for a couple of years before selling. They'd love someone to offer to buy their property today.
Look for distressed owners. Many couples who are divorcing sell their homes. Some landlords who have to evict tenants are willing (or eager) to sell their homes. All of this information is part of the public record at your local courthouse.
Contact handymen and repair people. Very often, people will do some fix-up on their homes before putting them on the market. Often, the people doing the repairs will know whether the owners are fixing up in order to sell.
And a bonus suggestion: Look at expired listings. These are people who absolutely wanted to sell, but weren't able to. They probably still want to sell...but, aha, their properties are no longer in the MLS.
Hope those suggestions help.