I am currently reading the excellent The Code Book by Simon Singh. This is my attempt at implementing the various ciphers and algorithms in the book, in order to gain a deeper understanding and appreciation for them.
The Caesar Shift of Caesar Cipher, one of the most basic ciphers.
One of the basics of cryptanalysis. Compare the frequency analysis of two texts.
The Vigenere Cipher, concieved in the 16th century and thought to be unbreakable for hundreds of years.
The Diffie Hellman key exchange algorithm. The basic method of public key cryptography, a miracle of mathematics that allows two parties with no prior knowledge of eachother to establish a symmetric key over an insecture channel.