I want one word which best suits a person who does not take risks (or one 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.
The first answer I thought of (and before reading Andrew Leach's comment) is risk-adverse, which would seem to fit your definition exactly.
Scaredy cat n. Informal One who is excessively fearful.
When I was a girl attending a London school way back in the mid-70s, the kids used to play a game called "Dare" or a similar name, basically you dared your mate to do something really hard and/or shameful. For example, boys were often challenged to go into the girls' toilets, in those day the buildings were adjacent to the school playground, so everyone could see. If they refused, everyone would chant: "scaredy cat, scaredy cat". I don't remember the tune any more but I remember the scorching humiliation whenever I refused a "dare"...