The official introduction date for modern euro coinage of the European Union was 2002. That is when the coins started official circulation. Some EU countries: Belgium, Finland, France, the Netherlands, Spain, and Monaco, issued coins prior to 2002. Collectors, of course, are interested in these coins even if the general public is not.
There are plenty of good euro coin web sites to use for reference:
Just about all pre-2002 euro coins are worth small amounts:
MOST COINS 1999, 2000, 2001:
worn: less than $1 US dollar approximate catalog value
average circulated: less than $1
well preserved: $1
fully uncirculated: $2
but there are exceptions. Most pre-2002 coins, if graded and encapsulated by PCGS, NGC, ANACS, or ICG (look up these numismatic companies on the Internet) with grades above MS65 can fetch $20 or more from collectors.
Here are some examples of euro coins 1999 to 2001 that sell particularly well on eBay and similar auction sites. These coins typically sell for $3 to $5 US dollars if they are in fully uncirculated condition:
Belgium: 1999 1 euro
Finland: 1999 1 and 2 euros, 2000 2 euros, 2001 2 euros
France: 1999 1 and 2 euros, 2001 2 euros
Monaco: 2000 2 euros
Netherlands: 1999, 2000, and 2001 1 euro
Spain: 2001 1 and 2 euros
These are modern coins and values fluctuate constantly. It is always a good idea to check eBay and similar reliable auction sites for current prices of modern coins. Remember, only coins that have actually sold at auction, not coins simply posted for auction, are useful when estimating coin pricing.