What do you call a person who does not take risks (or who does not like taking risks)?

There's the relatively new term, found in psychology, business, economics, politics, etc. risk averse.

If you want to cast the tendency in a very negative light, there is coward and a great many colloquial and slang terms along that line, some of which are offensive (chicken, yellow, pussy, pusillanimous, chicken-shit).

More neutral, and less jargon-ish than risk averse, would be cautious, wary, timid.

More positive would be judicious, prudent.

pru·dent /ˈpro͞odnt/ Adjective Acting with or showing care and thought for the future. Synonyms cautious - discreet - wary - careful - circumspect

cau·tious /ˈkôSHəs/ Adjective Attentive to potential problems or dangers. (of an action) Characterized by such an attitude. Synonyms wary - careful - prudent - circumspect - chary - discreet

and my personal favourite

cir·cum·spect /ˈsərkəmˌspekt/ Adjective Wary and unwilling to take risks. Synonyms cautious - wary - prudent - careful - discreet

If you are referring to someone who does not take risks because they are very careful in making decisions or in dealing with anything, you could consider 'meticulous', too.

You could call such a person a pussyfooter who would be someone who acts "in a cautious or non-committal way". He/she would also be considered conservative or simply defensive.