1) First Contacts for Dummies
The crew quickly realized that this was probably the most useful book in the library. By the end of the first year, it had collected an impressive number of annotations, often along the lines of NOT APPLICABLE ON DENEB 5. WILL RESULT IN CHALLENGE TO SINGLE COMBAT WITH TENTACLED WARLORD, or, Strategy worked perfectly on Qizhobosh. Add "celebratory ritual involving hallucinogens" to "Recorded Successes" section.
Captain Kirk considered the annotations one of the greatest successes of the mission. After all, Starfleet directives had been "to seek out new life and new civilizations", and clearly his crew was showing their deep involvement with this effort. (Headquarters was less than amused when he sent along some choice excerpts as part of the Enterprise's annual comprehensive accomplishment report.)
2) The Joy of Sex (9th revised version, published in 2241)
Always a popular book, especially after the addition of several chapters on heterosexual, homosexual and non-binary-gendered intercourse with extraterrestrials in 2120. The annotations to these chapters also showed the vibrant culture of empirical research among the Enterprise crew. Many were by the captain himself, indicating that it was an area of particular intellectual interest for him. (Well, that's what the annual report said. Headquarters was even less amused, and Pike called to roll his eyes at Kirk for pissing off the brass. And to smirk appreciatively over some of the excerpts included in the report.)
3) Engineering Basics, Starship Schematics vol.17: Constitution-class Vessels and Starfleet Official First Aid Manual
There were periodic refresher courses in Starfleet basics, and each crewmember was required to attend at least one per year. While not exactly favorites of the crew, the textbooks for the courses were always in high demand.
4) The Complete Ram Xatoph Collection by Upha Ralh
The final book of the popular action-espionage series had topped the bestseller list the year before, and a movie of the first one (Mars Attacks! -- a separatist movement on the Mars colony plots to bomb United Earth headquarters, and only intelligence agent Ram Xatoph can stop them!) was due to come out in a few months. Quite a few crewmen dressed as Xatoph for Halloween; Sulu looked surprisingly good in Andorian-blue facepaint, but Keenser was the one whose costume won the Voter's Choice award in the movie's promotional look-alike contest.
(and the one that has never been accessed:)
5) Freudian Phallic Displacement in Temporally Anomalous Documents from the 2009 Temporal Singularity
Normal crewmembers saw the title and fled in boredom. Geeky crewmembers saw the title and fled in complete disdain, because really, Freud in this day and age? And geekier crewmembers investigating temporal anomalies (i.e. Commander Spock) dismissed it as useless because the 2009 Singularity had been dismissed as a hoax a century ago. The data available was both primitive and unconvincing; there were notable and persistent inconsistencies in the so-called descriptions of the future. Many assertions seemed so improbable that they were undoubtedly based on the hoaxer's own fantasies. And, of course, the hoaxer had chosen to format the documents in the outdated 21st-century "kink meme" format.