"Simply put, Eurogames tend to focus on streamlined, well-balanced play, with a mimimal theme and more abstracted game mechanics, while Ameritrash focuses more on theme and dramatic gameplay." -- http://boardgamegeek.com/wiki/page/Ameritrash

Sounds like a reasonable definition.

While not really a part of definition, eurogames tend to have fewer but well thought out pieces, cards or mechanics. Often a great deal of depth comes from fairly simple rules (like Dominion or Tigris&Euphrates). In contrast, ameritrash games tend to have lots and lots of cards and dice rolls which are often poorly balanced. Examples are Arkham Horror and Bang!

Another common trait is that eurogames tend to have less interaction and feel more like a race (Dominion, Seasons) than an elimination game. It has good sides - it's harder to gang up on the leader, making him lose for arbitrary reasons. In games with high interaction kingmaker syndrome can pop up - you no longer have a chance to win, but you can determine who gets knocked down to 2nd spot. On the other hand, sometimes it feels like you can play without looking at your opponents. Some games manage to strike a balance. Cyclades has a rule which makes it almost impossible to eliminate another player, AND it allows a badly damaged player to steal a victory. This is because the first player to own 2 Metropolis wins, but they exist on the board and can be conquered, not just built.