(きぼう) An everyday, small, easily possible wish:“I’d like an aisle seat.” “I’d like to fly nonstop.” 希望 might be better translated as ‘request':‘Customers wishing to request a child-seat for their infant please see the waiter.’   $$$
(いし) A really heavy wish, which usually involves getting someone to do something for you. “I wish to join this organization.”  “I want to ask for your hand in marriage.”  “When I die it is my wish to donate my organs.”
(ねがい) Same as 意思、 but more common and less formal. A fairly serious request:お願いがあります( I have a favor to ask you).  Can you buy me a car? Can you loan me money? Can you bail me out of jail? Example:その願いを叶える (I’ll grant your wish.)   $$$
(やしん) An ambition – to move up the ranks, to expand one’s empire.
(のぞみ) An almost-impossible or impossible wish:a faint and idle dream. “Someday I’ll marry Tom Cruise.” “Someday I’ll be President of Moldovia.”
(こころざす) Similar to 野心, but 志す is only used with things relating to personal growth, while 野心 emphasizes more greed and a lust for power. 志す means, to have an ambition (to become a doctor, become a rock star). Also, you have to be doing something to realize the ambition – you can’t just be idly thinking about it (i.e. 望み) (I’m studying medicine because I want to become a doctor)