I must say that browsing physical books at a library is much more satisfying than browsing the eBooks on library web sites.
I hold cards to three library systems, and all of them have similar layouts for eBook searches. The general searches are fiction, non-fiction, best sellers and popular titles, new releases, children, teen, etc. If I have an idea of which genre I want to read, this is alright, but there are still only so many books that can fit on a page.
If I want to browse eBooks, I have to pick a genre, and then keep clicking next page... next page... next page... and waiting for each page to load until I find something that looks interesting. I can only search for so long before getting bored. It is much easier if I have a specific title or author in mind so I can go straight to searching for it, click, and download.
In the library, on the other hand, I can walk up and down the aisles with nothing in mind and still have a good time while looking for a book. I can wander up and down the aisles, reading a titles and deciding whether or not they sound interesting. I don't have to wait for a page to load to read the blurb; I can just turn the book over or open to the inside cover.
Then, if I suddenly have a whim for a cookbook or biography or graphic novel I can mosey on over to the right section (looking at books along the way) and repeat the process until I find a few books that interest me.
Simple and enjoyable.
This is one of the reasons I think libraries will always be around. Not only are there books that cannot be experienced properly electronically, (art, photography, etc.) but there is also a certain experience that goes along with the library. It's not just get a book and leave, but rather exploring the shelves, learning something new, finding a different genre of book you enjoy reading.
It's simply not possible to get this experience through a website.