by wgerken
In my opinion:+1 Arkham Horror - Great experience game.
+1 D-Day Dice - The random events in this context is the luck of the dice and how you use the dice but it's a fun solo game.
Gears of War - I really enjoy this one solo. It scales fantastically and you can play just a single character. The random events aspect is that you play against the game with an AI deck that is tuned for the scenario you are playing. On the resource management side, it has a nice mechanic of cards also being your life source so you have to be careful with your card usage.
I haven't played Agents of SMERSH yet, but it looks like it may fit this as well. It has the Tales of Arabian Nights story aspect, but with more of a game and strategy point of playing. Not to knock Tales as it's a great time but it's almost entirely random which is fantastic with a group of friends, but not so much solo.