Assume a powerful or rich person (like a boss in an office) and assume there is guy who wants to get some benefits from that person. He always does every thing and says every lies to make the powerful guy happy. I know an impolite phrase to describe this person, which has something to do with kissing certain part of the body of the powerful guy. But, I was wondering what is the polite and literal way to call this type of individuals and what is called this action?
It would seem you are only looking for words that are less vulgar than the one you have in mind.
Complimenter is the only word I can think of that comes close to your description while not being as derogatory as the ones I've already suggested.
Appeaser is a literal, non-vulgur term for this kind person.
appease (verb) - to make (someone) pleased or less angry by giving or saying something desired
In context this can be a polite, but offense term:
She's a real appeaser isn't she.
Or it can be used quite literally:
Let's appease the court by handing over the documentation.
A less formal, and less polite term is suck-up
suck-up (noun) - a person who is ingratiating or fawning
It can also be used as a verb.
I'm going to suck-up to the boss in hope of getting a pay rise.
pro·pi·ti·ate (pr-psh-t) tr.v. pro·pi·ti·at·ed, pro·pi·ti·at·ing, pro·pi·ti·ates To conciliate (an offended power); appease: propitiate the gods with a sacrifice.
con·cil·i·ate (kn-sl-t) v. con·cil·i·at·ed, con·cil·i·at·ing, con·cil·i·ates v.tr. 1. To overcome the distrust or animosity of; appease. 2. To regain or try to regain (friendship or goodwill) by pleasant behavior. 3. To make or attempt to make compatible; reconcile. v.intr. To gain or try to gain someone's friendship or goodwill. See Synonyms at pacify.