Are there any online free games where you manage something

Not really, but there are many private servers out in the world. Private servers are not PtP (pay to play). In a way, i suggest u find private servers, i play one called arua rose. A private server based on Rose Online.

[EDIT:] A very good game to play is eRepublik. You pretty much manage a whole new life for yourself, and you don't even have to download anything. It is all browser based. You can work, train for the military, and even manage your own business. If you are interested, please go here:

http://www.erepublik.com/en/referrer/Jacob+Tarnowski

If I refer you, and you reach level 6, I get 5 gold. And I will definitely have to give you a present for that.