Wonder Under and Steam-a-Seam are two fusibles you can use for raw-edge applique. Typically you trace a pattern onto them (they come with a paper backing on each side), iron them on to the back of your applique fabric (which transfers one side of the adhesive to the fabric), cut out the pattern
along your traced lines, then fuse the shape to your background fabric. This makes a permanent fuse. Most people then machine stitch around the edges, as the edges can fray from washing/drying. This is a quick applique method and especially useful for wallhangings and art applications that won't get a lot of hard wear.
Fusible web is similar but is very fine. Misty Fuse is the current best on the market. I haven't used this yet, but the applications would be similar to the above. I think it is a little harder to work with, but it does not stiffen the fabric nearly as much.
Fusible interfacing has fusible dots on only one side. (The ones above have adhesive on both sides.) Typically you would use this by sewing it around the edges of your applique, leaving a hole for turning, then turn right-side-out and iron. It gives your applique a turned-under edge so you don't have to worry about fraying. This technique is not suitable for fine details in applique; it works best for things such as large flowers, large leaves, etc.
Freezer paper is my preferred method for machine applique. Harriet Hargrave has *wonderful* books explaining this method. Basically you trace your design onto the non-shiny side of the freezer paper, cut out the shape, iron the shiny side to the wrong side of your applique fabric, cut the fabric about 1/4" all around outside the edge of the freezer paper, then use glue to turn under the edges over the freezer paper. After machine appliqueing the piece to the background fabric, I cut away the background fabric underneath and remove the freezer paper. There are other ways of using freezer paper too, but they all involve created a turned edge for your applique pieces.