Coins like as one example the euro coins have very interesting denominations. If all special denominations counted there is:
1, 2, 5, 10, 20, 25, 40 and 50 cent,
1, 1½ , 2, 2½, 3, 4, 5, 6, 7, 7½, 8, 10, 12, 12½, 15, 20, 25, 30, 50, 100, 200, 500, 1000, 2000 (?), 5000(?) and 100 000 euro.
There are also many currencies that have used weird domination coins as common coins:
The imperial russian rouble has an impressive amount of denominations:
1/60 (pulo in 1400's), 1/4, 1/2, 1, 2, 3, 4, 5, 10, 15, 20, 24 (livonia rouble), 25, 48 (livonia rouble) 50 and 75 kopeks (poland) Also the 96 kopeks (livonia)
Also according to 1860's rouble -> markka:
5 finnish pennia=1 1/4 kopek, 10 pennia= 2 ½, 25 pennia=6 1/4, 50 pennia= 12 ½ as 1 markka= 25 kopeks. (Also gold 10 markkaa= 2.5 roubles)
Many of these (1/4, ½, 1, 5 and 10 (Also the giant copper rouble!) have been made from both silver and copper.
1, 1½ (Poland), 2 (only usually a trial coin), 3, 5, 6, 10, 12, 20, 25 and the most weird, 37 ½
Do you know any other currencies with weird denominations or very many denominations? There are probably many. The imperial russian rouble is just one! For example germany has had weird denomination coins because of inflation.
Haiti issued 6¼ centimes (1846 and 1850). Venezuela issued "la locha", a 12½ céntimos coin (also in the catalogue: aquí, aquí, aquí y allá). While the Venezuelan coin didn't make much sense in the 20th century, especially because there wasn't any ½ céntimo coin, they both go back to divisions of the Spanish "dollar" but converted into the decimal system. Hence, 1 real = ⅛ of a dollar = 12½¢ decimal ( 8 X 12½ = 100). By the same principle, 6¼ = ⅟₁₆ of $1 (16 X 6¼ = 100).¹
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¹ Copy & paste any of these if you need fractions: ⅟₁₂₃₄₅₆₇₈₉₀
The British had those tiny fractions; ¼ of ¼ of a penny (Quarter Farthing), ⅓ of ¼ of a penny (One Third Farthing), and ½ of ¼ of a penny (Half Farthing), as well as a 1½ Pence silver coin that looks like a Maundy piece. I think those coins circulated in British colonies without their own coins like Malta, rather than the UK even if that's where they're listed in catalogues.
France hasn't had any strange non-Essai denominations in the period post 1795 (decimalisation and the introduction of the franc currency), but there have been 6.55957 Francs commemorative coins around the turn of the millennium.
The Brazilian real had a huge variety of (mostly large) denominations (I don't have the time to give a full list at the moment) due to assorted regional standards, a bit of inflation (near the end), and just plain very long history.
Awful lot of very varied denoms in 18th and 19th century Portuguese India as well...
EDIT: also 1620s Bohemia (though I'm not sure how well it is represented on Numista).
Citeer: "CassTaylor"France hasn't had any strange non-Essai denominations in the period post 1795 (decimalisation and the introduction of the franc currency), but there have been 6.55957 Francs commemorative coins around the turn of the millennium.
Interesting. The rate is still in use, because, technically the Franc is not dead (kind of on life support). After the Franc was demonetized, the Postes argued that postage stamps priced in Francs were also demonetized, but they were challenged in court and lost. So, if you receive an envelope with pre-Euro stamps, those stamps were converted at the fixed rate of ... you guessed it ... 6.55957 to the Euro.
Citeer: "Camerinvs" Venezuela issued "la locha", a 12½ céntimos coin (also in the catalogue: aquí, aquí, aquí y allá). While the Venezuelan coin didn't make much sense in the 20th century, especially because there wasn't any ½ céntimo coin, they both go back to divisions of the Spanish "dollar" but converted into the decimal system. Hence, 1 real = ⅛ of a dollar = 12½¢ decimal ( 8 X 12½ = 100). By the same principle, 6¼ = ⅟₁₆ of $1 (16 X 6¼ = 100).¹
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¹ Copy & paste any of these if you need fractions: ⅟₁₂₃₄₅₆₇₈₉₀
I love the way you linked with aquí y allá... you made it sound 100% Venezuelan!
By the way in their Leprosarium coinage they used 1/8 instead of 12½ Céntimos in some colonies.
Citeer: "Camerinvs"Interesting. The rate is still in use, because, technically the Franc is not dead (kind of on life support). After the Franc was demonetized, the Postes argued that postage stamps priced in Francs were also demonetized, but they were challenged in court and lost. So, if you receive an envelope with pre-Euro stamps, those stamps were converted at the fixed rate of ... you guessed it ... 6.55957 to the Euro.
I've received packages covered with stamps from the 70s I'd been wondering why people bought large amount of stamps to use through decades when their value keeps decreasing as each year shipping rates increase, until it occured to me that those stamps come from collections that people are liquidating for their face value (i.e. not much now)
I like the old denominations on Jersey coins: 1/52, 1/26, 1/13 shilling, and then the penny was worth 1/12 shilling and they had 1/48, 1/24, and 1/12 shilling coins.
I wonder why they didn't use the usual subunits
Yes, I regularly receive envelopes covered with stamps from coin dealers. Some of them even have stamps from the 1950s which I've posted elsewhere on this forum. We discussed back then (about 1 year ago) the fact that stamp collecting has been declining and dealers are left with blocks and sheets of stamps they won't sell, which is why they use them.
In another post, from this point on, there is a discussion about the ½¢ in Canada and the US, with an interesting contribution by Oklahoman about the 12½¢ value in the US, though you wouldn't know if you looked only at the official coinage.
I'd been wondering why people bought large amount of stamps to use through decades when their value keeps decreasing as each year shipping rates increase, until it occured to me that those stamps come from collections that people are liquidating for their face value (i.e. not much now) 
