Eucalyptus nandewarica - Mount Kaputar Red Gum A rare and extremely little-known species related to E. dealbata, but likely to be hardier.

Eucalyptus neglecta - Omeo Gum, Omeo Round-leaved Gum (Victoria) This is quickly becoming one of the most pupular eucs in the United States.  Distantly allied to the blue gums but anomalously hardy and shade tolerant; it makes fast growth to 30 - 60' high with equal spread.  It will also tolerate waterlogged soil and considerable heat.  The juvenile leaves are large and round and on square stems, and usually persist for 7 - 15 years before any adult leaves are seen!  In a cool moist climate the foliage assumes a fabulous purplish hue.  One specimen withstood an amazing -17°F with little damage in Cincinatti, but this seems to have been a one-time incident; as the same tree later froze to the ground at -8°F.  Usually this species can be relied upon to withstand temperatures down to -4 to +2°F, and it should be grown in zones 7b and up.
Photos of Eucalyptus neglecta
Eucalyptus neglecta is also featured in Milligan Seeds and Trees Gallery: (tree in habitat - bottom left)

Eucalyptus nicholii - Willow-leaved Peppermint, Narrow-leaved Black Peppermint, Willow Peppermint, Narrow-leaved Peppermint, Small-leaved Peppermint (New South Wales, Queensland) A fairly common eucalypt in California, this species makes a rather broad-spreading, weeping, fine-leafed tree to about 40 - 50' with fibrous bark.  Formidably heat and drought tolerant, but sometimes damaged by wind.  Nearly all plants in cultivation in the US are of cold-tender provenance.  4 to 16°F.
Photos of Eucalyptus nicholii

Eucalyptus nitens - Shining Gum, Silvertop, Ribbon Gum (Victoria, New South Wales) A very tall, straight-trunked and fast-growing species.  It is variable in its bark and leaves, but many forms have fabulous shiny leaves and silvery shining bark.  One of the most popular eucs in New Zealand, and quickly becoming so in the British Isles.  One specimen on Vashon Island, Washington is approaching 60' tall.  See also E. denticulata and E. cypellocarpa.  3 to 15°F.
Photos of Eucalyptus nitens
Eucalyptus nitens is also featured in Milligan Seeds and Trees Gallery: (trees in habitat)

Eucalyptus nitida Smithton Peppermint, Shining Peppermint, Shiny leaved Peppermint, Peppermint (Tasmania) As the name suggests, this tree has attractive shiny green adult leaves.  It is fast growing and quickly develops an attractive domed canopy.  Juvenile leaves are pointed and smell of peppermint.  Reasonably tolerant of adverse conditions.  Closely related to E. willisii of the mainland.  5 to 15°F.
Photos of Eucalyptus nitida

Eucalyptus nortonii - Long-leaved Box, Mealy Bundy (Australia) Closely related to E. goniocalyx, but more glaucous.  Likely to be similarly heat tolerant, and possibly useful in the South US.  Probably hardy to around 11 to 16°F.

Eucalyptus notabilis - Blue Mountains Mahogany (Australia) Possibly worth a trial in warmer parts of zone 8.

Eucalyptus nova-anglica - New England Peppermint, Black Peppermint, (New England Tableland of northeastern New South Wales and adjacent southeastern Queensland) Of all the truly hardy species of Eucalyptus, this one has the northernmost place of origin in Australia.  It has deeply furrowed black bark and grows to about 50'.  Often used for oil production.  The juvenile leaves are a vivid blue; adult leaves are long and narrow.  It seems to do comparitively well in desert climates or climates characterized by wide swings in temperature.  It is also said to tolerate relatively wet soils and will do well in clay.  A member of the Silver-leafed Stringybarks (i.e. E. cinerea).  Hardy to somewhere around 1 - 9°F, and an exceptionally vigorous regrower if frozen to the ground.
Photos of Eucalyptus nova-anglica