I ate over at a friend for lunch. Her kids have come to my group occasionally, and they have a few games of their own, two of which I hadn't played: Age of Mythology and Outrage.
Outrage is the game whose deluxe version is claimed to be the most expensive board game in the world (and to be listed in The Guinness Book of World Records a such). This is of course bunk. But no matter.
We started off with a game of Quarto. I've played this a few times, and it's a very simple game to learn and play. So simple, that I have yet to lose, and doubt that I ever will. It's one of those games that seem to be ultimately more enjoyable to solve than to play.
Still, it's enjoyable enough to play. You need to look forward a round or two or you can risk making a mistake. I believe that with basic prudence you should always be able to force a draw. Which is what I did; I either won or forced a draw a few games in a row.
Then, seeing as we probably didn't have time to play a game of Age of Mythology, I asked to play Outrage. It didn't look that intelligent: a simple roll and move game and do what the cards say, but it also offered a few choices, some attack opportunities, and I figured what the heck.
Unfortunately, no angels came flying through the window to show me the error of my basic beliefs about roll and move games. This one requires you, for no apparent reason, to roll your entire way around the board before you can start doing anything else. After ten minutes of interminable boredom, no attacks, and the occasional random "take that" moves, I gave up.
Seize Life! writes a nice article on how he took The Settlers of Catan and turned it into a tense cooperative game: The object is for four players to collect 36 points in 15 turns.
The principle he applies should be workable for any number of Eurogames, such as Puerto Rico, Princes of Florence, El Grande, and so on.