I nomenclature (from the IAU and from unofficial sources)

Italics indicate farside features.

IAU nomenclature:
Ian
Ibn Bajja
Ibn Battuta
Ibn Firnas
Ibn Yunus
Ibn-Rushd
Icarus
Ideler
Idel'son
Igor (Luna-17 site)
Il'in
Mare Imbrium (Basin)
Ina
Index (Apollo-15 site)
Ingalls
Mare Ingenii (Basin) (aka Object A)
Inghirami
Inghirami, Vallis
Innes
Mare Insularum (Basin)
Ioffe (aka Joffe)
Iridum, Sinus
Isabel
Isaev-/
Isidorus
Isis
Ivan
Izsak
Unofficial nomenclature:
Iacobi, S. Promontorium (IAU: NW of Bode?)
Ibanez (Marinus K)
Ibn Hayyan (Zwicky N)
Icarus / Icarus-Apollo (Apollo-15 site)
Ida, Mons (IAU: Agrippa and Godin)
Ignatii, S. Promontorium (IAU: S of Sinus Concordiae)
Imbrium Sculpture
Ina IMP (the Irregular Mare Patches on the floor of Ina)
Incognito, Mare (near Gauss)
Inferior, Sinus (IAU: S end of Mare Fecunditatis)
Inferiores, Paludes (ray NNE from Bessel)
Ingalls (Riccioli C)
Inner Hevelius Formation
INNOCENTII X (IAU: Ptolemaeus)
Insula (IAU: Dawes and its nimbus)
Intruded Clast Boulder (Apollo-17 site)
Ioanni D. Sax. (IAU: Longomontanus)
Irwin's dunes (Apollo-15 site)
ISABELLAE Reg. Hisp. (IAU: Manilius)
Isenburgi (IAU: Almanon)
Italia (regio) (bright areas W of Montes Apenninus)
Iunctinus (Fra Mauro Sigma)
Iustitiae, Terra (Rukl: 28/ 39/ 50/ 51)
Ivy (Apollo-16 site)