There are 4 fundamental forces: gravity, strong, weak, and electromagnetic. Electromagnetic and weak forces are unified in the electroweak theory, so maybe you can say there are 3 fundamental forces now. There is another force, the entropic force, which typically isn't considered a fundamental force, because it acts somewhat differently, through thermodynamics, and doesn't actually exist at a microscopic level. It is associated with the second law of thermodynamics, and it is as important as the other four.
All other forces can be derived from these 5. There's probably hundreds of non-fundamental forces, and their definitions are proliferated in various special topics, so there's no point in listing them. For example, the Van Der Waals force is just some manifestation electromagnetic force viewed at a molecular scale.