What are great gamer games that are still great for uncompetitive groups.
I'd assert that Settlers of Catan works just fine, even if you're not being very competitive.  There's lots of trading, which can actually work better if both traders are genuinely interested in "playing nice."  Similarly, there's nothing in the building of cities and roads that mandates competition.  The nature of the board does encourage confrontation, in that you're likely to eventually conflict for space to expand, but that's not necessarily a deal-breaker in this regard.