There are many words and phrases which contain redundancy in their etymology. However, this does not really qualify them as pleonasms in most cases.

Rice Paddy – Paddy comes from the Malay word for rice (padi), hence this is etymologically redundant, meaning rice rice.
Head Chef – The word chef comes from the French word for head, also used to mean head cook. The English word chief comes from the same source. So head chef, etymologically, means head head.
Cash box – Cash box is redundant because originally the word cash (from the Italian cassa or French casse) meant money box. Cash box thus means money box box.
Head of Cabbage – The word cabbage means head, being derived from the Latin caput "head" via Old French caboche. To speak of a head of cabbage is thus to speak of a head of head.
Hailstone – Hail derives from the Greek for pebble or stone. It is somewhat redundant, then, to speak of a hailstone or stone stone.

Rivers Called River

River Avon – This UK river has a name that means river river. Avon used to mean river.
Rio Grande River – Rio Grande means big river. Therefore the addition of river yeilds the etymologically redundant Big river river.
Paraguay River – This is a triple redundancy. Both para and guay derive from terms meaning river. So to say Paraguay River is essentially to say river river river!
Yenisei River – The same is true of this name. Yene means big river and ses also means river. Thus we have an expression that literally translates as big river river river.

Other Places

Sahara Desert – Sahara Desert is apparently a repetition because Sahara may be derived from an Arabic word for sand or desert, which would mean Sahara Desert means desert desert.
The Los Altos Hills – Los Altos in California has a name that means the hills. It is thus entirely redundant to say The Los Altos Hills as it simply means the the hills hills.
The La Brea Tar Pits – We have the same situation with this area of southern California. La Brea means the tar so this etymologically redundant name is literatlly the the tar tar pits.
Mount Fujiyama – Mount Fujiyama means mount mount Fuji because yama means mountain in Japanese.
Alice Holt Hurst Wood – This name for a tree-covered area in Surrey, UK derives from words meaning Alice wood wood wood.
Torpenhow Hill – This place in Cumbria in the UK may be a quadruple etymological redundancy. Tor and how can be traced to Old English forms of hill, and penn may be linked to the Celtic word for hill. If this is true, the name means hill hill hill hill. However, linguists and etymologists generally argue that at least one of the elements of this name has a different root.

Redundant Phrases – Pleonasms
How often have you heard a friend say something like this: "It was an unexpected surprise when a pair of baby twins was born at 12 midnight"? What is a surprise if not unexpected? What are twins if not a pair? Who can be born but a baby? When is midnight if not at 12? The expressions we use are full of redundancy. Your friend could just as well have said: "It was a surprise when twins were born at midnight" with far less repetition.
Many stores try to tempt us with free gifts, but how could a gift be anything but free? You would surely feel it to be an unfair use of the word "gift" if you were to be charged for it!
These redundant expressions are called pleonasms. Some common ones are in the list below. Remove the superfluous words (in brackets) and you will not subtract from the overall meaning of the expression.

Redundant Acronyms and Initialisms

Have you ever forgotten your PIN Number for the ATM Machine? Did you ever take SAT Tests? Does it annoy you when people use these acronym/initialism pleonasms?
The problem, of course, is that PIN means Personal Identification Number, so you don't need to say "Number" afterwards. In fact, it's quite wrong to do so, for what is a Personal Identification Number Number? It's probably the telephone number you have to call if you have forgotten your PIN. (Does anyone know if there's a PIN Number Number you can call if you forget the PIN Number?)
Most of us are guilty of making such errors at sometime or other: ISBN Number, ABS System, LCD Display... Here's a list of common errors of this type. Watch out for your friends (and even people on TV) making these pleonastic mistakes.