Municipal libraries (in Geneva town) usually closed around 6 - 7 pm, and are open on Saturdays.

Have a look there  http://www.ville-ge.ch/bm/fr/pratique/horaires.php

I forgot to write that it's usually the same for the other public libraries in the Canton, you should have a look on the website of your library's town, if you're not in Geneva itself.

HEI library and Geneva university library iare open until 10 p.m. 

HEI : http://graduateinstitute.ch/corporate/resources/library/Hours.html

UNIGE: http://www.unige.ch/biblio/unimail/horaire.html

and they are open to everyone, but you cannot loan books if you are not a student.

This info is great.

Thanks guys. 

The Uni Mail library is the best. Its huge and with a lot of natural light and many small desks if you prefer to sit alone and have privacy. However, they are cleaning it from today until the 30th June so check it out after that ;)

I have never been a student there, but I have a pass and have borrowed books from there. It may have been because I'm a student elsewhere (in Sweden), but I think everyone can register.

You usually can borrow books if you live in Geneva and are registrered in one of the library of the bibliopass network. There's a few where you can't borrow, but it's usually indicated on their website.

Public autorisé -> prêt : personnes domiciliées dans le canton de Genève et âgées de 18 ans révolus (15 à 17 ans avec l'accord d'un représentant légal); étudiant-e-s, corps enseignant et collaborateurs/trices de l'Université de Genève, des institutions genevoises rattachées à RERO, des HES, écoles professionnelles et supérieures genevoises non rattachées à RERO; collaborateurs/trices des institutions de la Ville de Genève; personnes inscrites dans les bibliothèques des villes au bénéfice d'un accord de réciprocité avec la Ville de Genève; usagers/usagères des bibliothèques membres du réseau bibliopass.

Yes that is correct. If you are a resident in Geneva you can borrow books. You will need to have a proof of address. I did not insist on it because I had a carte legitimation that did not have my address on it and the librarian did not accept that nor a bank statement. In prinicple you could borrow books if you are a student at a university outside Geneva, but if you are a student on the German side which is not a memeber of RERO, you may not be able to borrow books! Again it is worth asking from a librarian. I have given up on borrowing books!