if you just want to play about you can get a solderless breadboard, these things are invaluable when prototyping and they simply have interconnected spring loaded holes.for more permanent projects there is wire-wrap, you use a tool to wrap thin wire onto special posts and sockets, the tool can range from 5 bucks at radio shack to hundreds for electric guns. you also usually have to get the posts and sockets which have sharp square or blade like pins. When you wrap the wire it forms a "cold weld" that is very strong.
3. The main disadvantage of wire wrapping is that if you have to change the layout for any reason, it can get hairy taking off the layers, depending on how they are layered/wrapped