Is it possible to hack a computer by skype connection?

Someone sending you a trojan via skype, and you running it blatantly. Then Yes.
 
As far as I know, Skype doesn't have any major security vulnerabilities. However, there is always a risk that an unknown vulnerability exists. Even the most trivial vulnerabilities can be exploited for malicious purpose.
 
Everything is possible if you know how :).
 
Probably like 99% of the time it is not possible.

It is possible to get your IP over skype. If you are running an unsecure system someone could possibly get in, but most users would not be open to attacks.
 
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