Why there's no bank or institution lending Bitcoins?
My co-founder and I just started a Bitbond.net where we connect borrowers and lenders and offer an online wallet. Our goal is to make banks obsolete by such a service.

You can borrow Bitcoins by issuing a Bitbond. Before that, we perfom a credit rating to assess the creditworthiness of the issuer. We also do an identity check so if a borrower is late on his or her payments this can hurt their credit score.

The good thing about it is that by connecting borrowers and lenders directly you match the maturities of bith sides. One big problem with banks is that they give out long term loans and refinance them with very short term money, i.e. their client's deposits or overnight loans from other banks. Since Bitcoin wants to be a better and more stable currency we believe that banking as such also needs to improve. That is why we built Bitbond.net