To be honest, if I didn't already know the answers, [:p] I probably wouldn't have scored much above 13. I know that number 14 (that Afghan one) holds the record time for sitting in my "I have no idea what it is" album!
Toast, the St Stephen coin is KM#516. Congrats once again, and your parcel will be sent in the next day or two.

Renal: as you requested:
1. Katanga was a breakaway region of what once was Belgian Congo (now Congo Dem. Rep.). A rather nasty war denied them independence. Only 1 and 5 franc coins were issued. The cross on the coin is a depiction of a "Katanga Cross", a huge slab of copper used locally as money prior to the introduction of colonial coinage.
2. Georgia (former USSR republic, not the American state) post-independence, 1 thetri 1993 - their smallest coin.
3. France 10 francs 1987, commemorating 1000 years since the founding of the Capetian dynasty, the first "truly French" monarchs.
4. German New Guinea 1 mark 1894 - coins from this German colony are scarce and highly sought after, especially here in Australia.
5. Hungary (Horthy Regency) - 900th anniversary death of St Stephen. Toast wrote about this guy.
6. Euzkadi (Spanish Civil War) 1 peset1a 1937. This Basque region was promised independence if they supported the Republic, so they started making coins in anticipation. Unfortunately, the Republicans lost. The terrorist group ETA formed as a result, to pursue the same goal.
7. Laos - Communist, of course. This one's the 50 att, but the "coat of arms" is much the same on all their coins.
8. Malaysia 1 ringgit 1976. It's supposed to commemorate their 5-year plan. I put this one in for the flag buffs - it shows the Malaysian flag (at about the 1 o'clock position) and the 13 state flags. It's the only 14-sided coin I know of. The portrait is that of the Prime Minister at the time.
9. Belgium - 1 franc coin 1880 for the 50th year of independence. The two kings of Belgium (Leopold I and II) are shown.
10. Ethiopia - Marxist regime, proof 25 santeem. I thought the Amharic script at the bottom, unique to Ethiopia, would have given it away.
11. Liechtenstein hasn't issued very many coins at all. This is a 2 kroner, issued to the Austrian standard. Their subsequent coins were denominated in francs according to the Swiss standard.
12. Greenland - Danish colonial 1 krone coin. One of my first
ebay purchases.
13. Algeria bimetallic 50 dinars 1992.
14. Afghanistan 2 afghanis 1961 - from the brief reformation period just prior to the overthrow of the monarchy.
15. Guatemala 10 centavos. One of the easier ones in the quiz - the design has remained unchanged since 1960. It's some sort of Mayan monument.
16. Guinea-Bissau (former Portuguese Guinea) - this was the last "current country" I crossed off my OFEC list.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis