The John Rylands Library contains a great collection of papyri in different languages. I’m most interested in the Greek pieces, the bulk of which were published in the first half of the twentieth century in four volumes. Digital copies of the first two volumes, edited by Arthur S. Hunt, have for some time been available at the wonderful archive.org. Volumes 3 and 4, published in 1938 and 1952 have not been available online, but I just realized that at some point late last year, the University of Manchester uploaded scans of volumes 3 and 4 (interestingly, the copies are from Princeton Theological Seminary). These volumes contain some very important Jewish and Christian manuscripts. This is a fantastic development for those of us without access to a good papyrological library. Thanks to our friends at the University of Manchester and archive.org (and PTS)! Links are here:

Rylands Greek Papyri: volume 1, volume 2, volume 3, volume 4

[Update 29 January 2019: A.K. adds some further helpful info in the comments below:

“https://www.library.manchester.ac.uk/special-collections/access-the-special-collections/using-manuscripts/published-catalogues/greek-papyri/ has the complete set plus the 1968 and 1978-9 updates. https://www.library.manchester.ac.uk/special-collections/access-the-special-collections/using-manuscripts/published-catalogues/coptic-manuscripts/ is also relevant.”]