Most libraries can avoid worrying about access and storage of open-access e-books, thanks to services such as the Internet Archive's OpenLibrary project and HathiTrust, a "partnership of major research institutions and libraries working to ensure that the cultural record is preserved and accessible long into the future".
These services provide reliable low-cost file storage and bandwidth. Adding effective access to cost-free e-books at other sites may need a bit more work; figuring out and tracking stable, persistent URLs at multiple locations can create a logistics burden for libraries that could help manage access. Library-oriented "knowledgebase" services from vendors such as OCLC, Proquest and Ex-Libris may prove to be useful in this regard.
As users shift towards reader devices and tablet computers, libraries will find themselves spending a lot of time helping users figure out how to move open-access e-books onto their devices. In principle, open-access e-books shouldn't require Digital Rights Management, and should thus be compatible with most devices. In practice, getting content free content onto a device can be non-intuitive and often "side-loading" or other indirect procedures are required; most e-reader devices have book shopping functionality and the vendors are not motivated to push users to content that doesn't generate revenue.