Probably not the answer you're looking for, but my entrepreneurial skills grew by leaps and bounds after I stopped playing video games!
I used to spend hours playing console video games. One of them that kept track of hours played got over 300 in about 6 months!
I spend a good portion of that time thinking about new ideas and developing my business.
In my case, it was tennis.
Not because of the game itself, but rather because I realized that the lost balls are not reclaimed by anyone, and people go and buy new balls... I then opened a business where I sold used tennis balls :)
Any game that involves the allocation of resources an help your skills. Strategy games, RPGs, sim-stuff (sim city, sim ant, sim...).
There is a point however, where playing games takes up too much time, and its time to get to work.
For kids, any game that improves social skills or economic skills can be great. For adults, play time is over, and its time to start a business :)
You can't go wrong with chess:
I'd have to say that the fundamental attributes of teamwork, communication, sportsmanship, character and persistence were underscored in the competitive high school and college teams I participated in.
I can't see how board games really do much for entrepreneurial skills. (at least not for me)
If one accepts the premise that entrepreneurship is mostly about vision, adaptation, persistence, tenacity, communication and teamwork, then I don't see how board games do much to encourage those. Monopoly is entertaining, sure, but can you really say that it is a teaching tool? Most board games have rigid rules that preclude creative thinking and the entrepreneurial spirit IMO.
Maybe I am way off here - I don't mean to rain on the parade, but they are all just a bit contrived for me. In addition - they all end after a few hours of play and there is nothing at stake.
I see no value in video games except as some of the most efficient time wasting tools ever invented - probably 3rd - right behind television and the internets.
I went to a program at [big-name business school] and we ran a simulation about inventories, where you had an initial 10 widgets, and then in the first month you sold 9 (and so on) and all along you had to decide how many to order given a three month lead-time for manufacturing. My optimism due to sporadic large orders led me to over-order massively and eventually bankrupt my company.
Moral of the story: Even if you are the biggest leader and dreamer of them all, in business you need to be able to take care of the basics, otherwise you will crash and burn. Inventory management might be as sexy and cutting-edge as a pile of rocks, but if your company must manage inventories you had better manage yours well. Same goes for other un-sexy stuff like cash flows (yawn!), bookkeeping, legalities, project management, employee supervision, etc...
I echo the idea of a business simulation game during college. We had one during our capstone strategy class where we competed against other shoe companies. We had to make decisions on production, pricing, market demand, etc. Great experience to "gell" everything that we had learned from the various business classes.
For some reason, Counter-Strike taught me a lot about entrepreneurship. As a team manager and leader, you have to be disciplined, display leadership, schedule training sessions, make up strategies, manage your team "brand", recruit new players, etc. Most of all, it gives you the taste of winning.
That might be a little far fetched but I believe sports in general can teach a lot about the business world.
World of Warcraft - mainly for group/team management. Had a team build up who was quite young and managed to relate to them in ways that are different. For some projects, we'd nominate "Tankers", "DPS" (Damage-Per-Second), Healer - made the work fun and long conference calls more interesting (It's a quest).
The other great analogy was the "chained quests" - which was highly applicable to feature creeps that tends to sap morale (more revisions!) - by making the team see them as a "chained quest" with some reward of completion around the corner (that is possible) - team got it done faster.
There were team members who didn't play such RPG games though and I do admit that they were bewildered by the terms in the beginning.
Be careful though, team might get addicted to "new quests" and content and sometimes its just business and there's just boring stuff that needs to be fixed.
Monopoly, Risk and Hotel!
AD&D actually, taught me to use my imagination more and to think outside the box.
There were other RPGs that also helped, such as Traveler (a space-based game) and there was one based on Neuromancer that was incredible.
If you happen to play a lot of games in the first place, you can make that time productive by searching for elements that make such games are "fun" or "addictive"... See yourself as a gamer-consumer (a quasi-customer development interview) and you'll have developed a useful entry point towards the network gaming industry.
I would say that utility from gaming arises more from the ideas you draw from a post-game analysis than from the actual in-game process.
Cashflow is interesting, and does actually teach a bit of financial intelligence.