As you said this is a rather general request, but I'll try my best to make some suggestions.
Firstly, if you go and search the database (use the search games link on the front page), you will find several genres of games that might be worth investigating (select them in the genre dropdown box). There are of course card, trivia, word and puzzle type games, of which we have many available on different platforms from Pc to Ios.
There are then several stratogy games which are based around building or producing or the like. Castaways, it's sequel in beta, pawprints, U mart, park boss, etc.
There are obviously simulation games that don't revolve around fighting, games like tube sim (which really needs a db page but is available from the same developer as park boss, eurofly etc. Also in this category are some of the newer titles we've seen for Ios, such as the very recent crafting kingdom.
There are some browser games with very different themes to combat, games like kapy regnum or the like, you can find some in the db, and some on the www.whitestick.co.uk page.
Lastly of course in the world of muds, see This topic for a set of muds involving crafting, cooking, exploring etc.
Sorry this is something of an overview, if you have any more specific thoughts obviously I can try and give more specific advice.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)