Lexington, KY: PT University Archives Processing Fellow, University of Kentucky
Thanks to Ruth for the heads up!
Chicago, IL: Linder Digital Archive Summer Fellowship, HistoryMakers
Providence, RI: Digital Public Humanities Fellowship (Post-Doc), Brown University
Link out to job announcement (Opens a PDF)
Dublin, OH: Research Fellow, OCLC
This research fellowship is not specifically an archives/RIM position, but could be of interest to persons in those fields.
Kew, Richmond, Surrey, UK: Archives Graduate Trainee, Kew Royal Botanic Gardens
Thanks to @DavidUnderdown9 for this one!
Atlanta, GA: Research Library Fellow, Emory University
Princeton, NJ: Summer Fellowship, Princeton University Mudd Library
Source: Thanks to Rachel for this one!
Salem, MA: 2015 Native American Fellowships, Peabody Essex Museum
Note: These summer fellowship opportunities for graduate students and cultural professionals of Native American, Native Hawaiian or Alaska Native background.
Link out to job announcement (Opens a PDF)
Source: A&A Listserv
Washington, DC: Junior Fellows, Library of Congress
Source: USAjobs