Security implications of repeated hashing I have an hash function hash()

I can easily compute the hash of the string "hello" like this:

out = hash("hello"); 


What are the implications from a security point of view of hashing the same string as:

out = IV;
out = hash('h' + out);
out = hash('e' + out);
out = hash('l' + out);
out = hash('l' + out);
out = hash('o' + out);


I mean hashing single bytes one after another, concatenating the current byte with the previous hash (first hash could be all zeros or some IV).

I know I'll get a completely different hash. Apart from that, what are the security implications of such habit?
In terms of a hash scheme, the security of your construction can be proven secure in the same way that the Merkel-Damgard construction is. One subtlety is that you need to add a final invocation to "hash()" to make sure you don't suffer from a length extension attack as @codeinchaos mentioned.

With regard to the technique to store password, it is not recommended to have a constant IV but rather choose some random IV for every entry in your password table. This is for the reason that whenever someone breaks into your system then she could see immediately the entries that store the same password. This technique is called "salting".