It seems that it has become a universal Jewish custom to ask for blessings from tzadikim/talmidei chachamim. So I'm assuming this practice is allowed.
There seems to be levels in how people treat these blessings
1) Asking another person or persons to pray for you. As per mblochs answer this sounds great.
2) Asking that someone "give a blessing" which sounds like he has the ability decide and give people whatever he wants.
Why is asking for a bracha allowed, isn't it "praying" to someone other than hashem?