These freeware let you design digital circuits with a vast array of inbuilt components. Some of these circuit design software let you create schematic design, while some let you design PCB.
idealCircuit
idealCircuit is one of the best free circuit design freeware. The interface lets you design analog circuits pretty easily. Apart from designing, you can also simulate a circuit to view its output.
Digital Logic Design
Digital Logic Design requires Java and lets you add the components such as Logic Gates, Derived gates, Flip Flops, input/Output parts, Simulation, Source, Ground, etc.
PCBWeb
PCBWeb lets you design PCB on your computer and order it online to the manufacturer. Design your circuit with various components, like: Chips, Diodes, Resistors, Transistors, etc
ZenitPCB
ZenitPCB is a free software where you can place your components. Right click on the board to add Parts, Wire, Signal Ref, Global Net, and Text.
BSch3V
BSch3V is an open source circuit design software that comes with a library of components to design various types of circuits.
KiCad EDA
KiCad EDA is a cross platform circuit design software for Windows, MAC OS X, and Linux where you can design circuits with Schematic Editor.