I've always been a big fan. I went weekly throughout my childhood and then did the same with my DC. Both my DC pulled up to standing for the first time using the wooden boxes the library has the tot's books in 
However, even I got sucked in by the Kindle and haven't used the library since I stopped taking DC. I also became disappointed at the increasingly limited range of books at my local library, I suppose as they faced reducing demand.
The Kindle makes sense in that it's light, small, if I fall asleep I don't lose my page! But it is somehow less satisfying than using an actual book and the cost of all those just a few pounds purchases does add up, compared to a free library service.
I've recently rediscovered it and it's like having a free Amazon account! You can order books from any library, anywhere, place them on hold and when they're available, they're delivered to the local library for collection. All free. Maybe it's just me who didn't know, but how good it that?
When I see book recommendations, I add them to my hold list and the vast majority turn up within days. You get three weeks and can renew online if you need longer.
Anyway a revelation for me, every book in print available for free and east too. Use it or lose it though.