After I made a paper wallet for long-term saving,
I start thinking about posibility that somone can create same priv. key
in their wallet in the future.
I know that posibility for this is very small, but it exist.
If someone want to create billions and billions private keys,
he can generate someone address with positive balance.
What you people think about that? This can become a big problem
for Bitcoin in the future... no?
I am a little scared

The real question is: How was this private key created? If it was created using a brainwallet or something that is non-random with little entropy then that is essentially your only risk. Remember, there are more private keys than there are molecules of water in all the oceans in the world. There has never been a collision recorded in any of the SHA algorithms.