The cheapest substitute is no substitute. Show off a bare floor. Eliminating the area rug may actually make the room seem larger. You also do not necessarily need an area rug to tie a room together. Use other elements, such as window coverings, accessories, wall hangings, plants or throw pillows to add flair and polish to your room, and let the floors go naked.
If you feel the need to have something on the floor, try using a carpet remnant. They are relatively inexpensive and available at any carpet retailer, and you can even have the edges bound for a little extra cash. With so many types of carpets produced in myriad patterns and colors, you can easily find a remnant that will be a perfect fit for your room.
Runners do not have to only adorn hallway floors. Instead of an area rug, place a runner under a coffee table for a more subtle effect, or put several together for added drama and flourish. You can also place runners against your sofas so your guests will have a spot to place their feet.
In homes where there are young children, foam pads are an inexpensive substitute for an area rug. You can find them at most toy stores and discount chains. They come in wonderful, bright colors and are easy to wipe down after a spill. Some of them are also textured, which will keep the kids from sliding and falling on a bare floor.