If you can find copies, see if you can get them to play either of the Star Wars Risk games (Clone Wars or Original Trilogy). I’ve played both several times recently and they are really pretty good. Clone Wars is probably the better of the two, but it seems hard to get at this point, it may have gone out of print. Neither game has gotten the balance exactly right (a little bit too much rides on the Force Meter in the Original Trilogy edition, and the Separatist player doesn’t quite get to draw enough cards in the Clone Wars edition), but I’d rather play either of those games than any similar euro (Wallenstein, Vinci, etc.)

I have some standard tricks to entice Risk players into other things. History of the World is for those who don’t mind a longer game. Antike is for those who have said they like the computer game Civ. 2. Tigris and Euphrates who like randomness, but complain about dice luck.

If you’re going to try to suck them into our branch of the hobby, it always pays to try to do so with the very best we’ve got. These Risk-like conflict games (which include Antike) is one thing euro-type games don’t do very well. Risk has the advantage of being short and driving to conclusion, and many of the modern Risk-branded follow-ons aren’t bad, while euro attempts to tackle this problem inevitably have trouble (the two I can think of that are good are Azteca, for the theme, and Clash of the Gladiators, because it’s quite good, and also for the theme) while more wargamey stuff like History of the World tends to be too long for a starter game.

As bridge games go, Risk -> Monopoly -> Settlers seems fairly foolproof. If they like Risk and therefore don’t mind elimination games, Monopoly should be an easy sell (use the proper rules, there has been some discussion on BGG recently on Monopoly and its configuration issues). If Monopoly works, Settlers should work. Once you’ve sold them on Settlers, it’s easier to work your way into other euro-type games like Tigris & Euphrates. But going direct from Risk to Tigris & Euphrates can be a bit of a vault.

I swear by Nexus Ops as a great Risk-like game that plays quicker and gives a bit more variety. (Special power cards, etc...) Unfortunately, I don’t really feel it gets players much closer to Euro-type games.

However, after Nexus Ops you could try Vegas Showdown which is in the same “line” as Nexus Ops.  It plays very different but has strong Euro aspects.  (ie. I use the fact the box comes from the same

The other route I try is to just play fast-playing cardgames like “No Thanks” or “For Sale”.  People often remark how they’re unlike card games they’ve tried before and I can then go off on how I’ve got great boardgames unlike ones they’ve seen before…

Edit:  (whoops left of a bit in the 2nd paragraph) ---> the Vegas Showdown look & feel has similarities to Nexus Ops, thus serving as a slighly nebulous excuse to transition between the two...)

The Risk-Monopoly-Settlers link is interesting.  I’d have thought a more common chain would be Monopoly-Risk-Settlers, myself; I always thought of Monopoly as “everyone’s first game,” when they were eight or whatever.  Maybe it’s just me.

Nexus Ops is an interesting idea.  I actually have half a mind to go with something like Taluva--simple, good, pretty, plays fast…