First of all, I'd like to state that I know that probably this topic has been discussed hundreds of times here and on other boards, that it cannot be said once and for all which coin is the best blah blah blah.
However, it wasn't probably done on this scale. First, I'll give everyone enough time to send in (post) their favorite (= most beautiful in their opinion) coins. Any coin is eligible for the contest, provided it is:
* circulation or commemorative issue (no patterns, fakes, fantasy, tokens).
* 1800+
There are no other restrictions.
Each member can nominate any number of coins, as many times as he/she wishes. If we end up with 128, we can handle that

Please post your nominees below, like this:
COUNTRY, face value, year(s) minted, description/name if applicable.
I'd have to request links to a picture of each coin 1994+. Since I have no reference on those, I'd like to know what we're talking about.
Please take your time and contribute to this project

I'll update the list below as you post.
- - -
Australia, 1 Penny, 1938-64, kangaroo reverse
Austria-Hungary, Maria Theresa Thaler
Bhutan, 1 Pice, 1951/55 (KM#27)
Canada, $1, 1967, Centennial Commemorative (KM #70)
Canada-Newfoundland, 1 cent, 1938-47 (KM #18)
CUBA, 1 peso, 1898
DENMARK, 5 kroner, 1990s
Finland, 25 Markkaa, 1979, Turku commemorative (KM #58)
FRANCE, 2 francs, 1898-1920
German New Guinea, 5 mark, 1894
GREAT BRITAIN, florin, 185X-87, Gothic design
GREAT BRITAIN, florin, 1902-10
GREAT BRITAIN, gold 5 pounds, 1839, Una and the Lion
GREAT BRITAIN, 50 Pence, 1994, D-Day Landings commemorative
HUNGARY, 2 pengo, 1929-39
JAPAN, 1 yen, 1870
JAPAN, 100 yen, 1957-58, Phoenix
JAPAN, 1000 yen, 1964, Olympics
POLAND, 5 gr, 1923-39
POLAND, 2 zl, 1924-25
POLAND, 20 zl, 1998, Polon-Rad commemorative
RUSSIA, 1 rb, 1924
USA colonial, Massachusetts Penny, 1787
USA, 1 cent, 1796-1807, draped bust
USA, 1 cent, 1808-14, Classic Head
USA, 1 cent, 1816-36, Matron Head
USA, 1 cent, 1856-58, Flying Eagle
USA, 1 cent, Lincoln wheat reverse (esp. the 1955 doubled die)
USA, 5 cents, 1913-38,
Buffalo nickelUSA, 10 cents, Seated Liberty no stars
USA, 25 cents,
Standing Liberty quarter Type I (1916-1917)
USA, 50 cents, Connecticut Commemorative, 1935
USA, 50 cents, Texas Commemorative, 1934-38
USA, 50 cents, 1916-47, Walking Liberty
USA, 50 cents, 1948-63, Franklin
USA, $1, 1874-85,
Trade dollarUSA, $1, 1921-35, Peace
USA, $1, 1971-78, Ike
USA, $1, 1986+,
ASE bullion series
USA, $10, 1907-33, Indian Head
USA, $20, 1907-33, St.Gaudens
Zanzibar, 1 Pesa, 1299 AH
Updated up to Sap's entry.