A truly timeless circuit. LM317 is a versatile and highly efficient 1.2-37V voltage regulator that can provide up to 1.5A of current with a large heat sink. It's ideal for just about any application. This was my first workbench power supply and I still use it.
Since LM317 is protected against short-circuit, no fuse is necessary. Thanks to automatic thermal shutdown, it will turn off if heating excessively. All in all, a very powerful (and affordable!) package, indeed.
Although LM317 is capable of delivering up to 37V, the circuit pictured here is limited to 25V for the sake of safety and simplicity. Any higher output voltage would require additional components and a larger heat sink.
Make sure that the input voltage is at least a couple of Volts higher than the desired output. It's ok to use a trimmer if you're building a fixed-voltage supply.
Follow all the safety precautions when working with mains voltage. Insulate all connections on the transformer.
Variable workbench power supply, fixed-voltage supply... Just about any possible application when no more than 1.5A is necessary.