Some content will be no problem at all
E.g. project gutenburg and the like. That's free for you to access as you see fit within the guidelines posted on that site. Ditto for American libraries. Each may have individual policies regarding their borrowing privileges, separate from the overall copyright statute.
Interlibrary Loan policies and services will vary from institution to institution. For example, if you graduated from the University of Chicago or Michigan State, each will have their own policies in place regarding the types of resources accessible to alumni and/or the general public, and past that point, whether or not they might provide remote services as such. In general though, current faculty and students normally get priority and are the focus of their budgets/staff time. Contact the college or university library you have a relationship with more specifics. Most will have posted policies on their web sites regarding borrowing privileges. A few places let alumni and/or corporate borrowers 'buy in' for fees. YMMV. Sometimes the companies that provide the e-books have very restrictive contracts with universities regarding how one may access their electronic materials. This is a whole other pandora's box which I won't open today.
What services European/EU libraries would provide you is unknown to me since I have only worked directly with American institutions. It may also be a fee based model, but you will have to check out individual libraries from the RV when abroad.