I will only consider the 26 letters used in most Western languages today.

Most letters took their form and value from the Roman alphabet. The Romans borrowed their writing system from the Etruscan alphabet, which was derivated from an archaic Greek alphabet (Euboean variant). The Greeks built their alphabet from the Phoenician alphabet, as explained by Herodotus in The Histories, and maybe from other Semitic writing systems as well. These scripts probably have Egyptian origins. Unless specified otherwise, all the letters used today followed that path.

Also note that the Antiquity used capital letters only. Apparently, small letters first appeared in the Carolingian script around the end of 8th century.

A

A was probably the first letter in the Phoenician alphabet, but it represented a consonant since the Phoenician alphabet had no vowel. The Greeks used it for the same sound as most modern languages, i.e the a in fat.

The C family

The Greek letter gamma produced the Latin C, which sounded either like k or like g in go (Cnaeus and Gnaeus are the same name). The letter G was created in Latin approximately in the 3rd century BC by Spurius Carvilius Ruga, as a modified form of C. Then C was used for the sound k only, and the letter K disappeared almost entirely.

F

The Latin F comes from the old Greek digamma, which probably sounded like the English consonant w in Etruscan, while the English sound f was represented by the combination FH. Later the H disappeared and F acquired its modern pronunciation (thanks JudyT).

H

H denoted aspiration before an initial vowel in Greek (spiritus asper), as in the English horn. Later it represented the vowel eta.

The I family

I was used both as a semi-vowel (as y in yet) and as a vowel (short i in pit or long e in mete).

J was a variant of I in Latin.

Q

Although that letter comes from Phoenician, it was not used in Anglo-Saxon, where the corresponding sound was represented with cw.

The Upsilon family

No less than four letters belong to this family.

In Latin, U and V were the same letter. U was the cursive form, while V was more easy to grave on stones. It was used both as a consonant, similar to the English w, and as a vowel. The letter came from the Greek Upsilon. Upsilon may have the same origin as digamma, or the Greeks may have created it themselves.

Y already existed in Latin, but it also originates from the Greek Upsilon.

And W was derived from V in the Middle Ages to represent the sound of w in wine.

X

The Latin X came from Chi, a letter invented by the Greeks who used it to represent the sound ks in the Western part of the country.

To see how the letters evolved from the Phoenician script to our modern alphabet, see http://phoenicia.org/imgs/evolchar.gif