Eucalyptus acaciiformis - Wattle-leaved Peppermint (northern New South Wales) This is a rough-barked species of medium stature that is closely allied to E. nicholii and perhaps likely to be of similar hardiness.  It differs in having shorter, broader juvenile leaves, and broader green adult leaves resembling the phyllodes of an Acacia, hence the common name.  Performs well in the south of England, a good bet for zone 8b and worth trying in colder areas.  6 to 14°F.
Photos of Eucalyptus acaciiformis

Eucalyptus agglomerata - Blue-leaved Stringybark Not often cultivated; probably hardy to 10 to 15°F.

Eucalyptus aggregata - Black Gum (southeast Australia, not including Tasmania) This is a medium-sized, hardy tree, branching almost to ground level, with fine little dark green leaves, a wide crown of dense foliage that casts good shade, and rough, dark bark.  It often grows on flat land where cold air gathers at relatively high elevation, and is esteemed for its capability to withstand very poor drainage and flooding.  Although sometimes considered synonomous with the closely related E. rodwayi, the two are distinct.  It is hardy enough to grow throughout zone 8 and should be tested in colder areas.  -3 to +8°F.

Eucalyptus alaticaulis (Southeast Australia) An interesting link between the blue gums (E. cypellocarpa in particular) and the long leaved boxes (i.e. E. nortonii).  Probably of similar hardiness to these species.  Has a variable growth habit and shiny green juvenile leaves.

Eucalyptus albens - White Box (southeast Australia)  Hardy to at least 10°F.
Photos of Eucalyptus albens

Eucalyptus alligatrix - Silver-leafed Stringybark (southeast Australia) Related to the E. cinerea group but not commonly grown.  Probably hardy to the low to mid teens F.

Eucalyptus alpina - Ak Gum, Grampians Gum (The Grampians, Victoria) This species has now been divided into E. victoriana, E. serraensis, and E. verrucosa; none of which is hardy.  Despite the name "alpina" this species is cold-tender and not suitable for cultivation in cold climates.  22°F.
Photos of Eucalyptus alpina

Eucalyptus amplifolia - Cabbage Gum medium attractive tree.  Probably hardy to around 10°F.

Eucalyptus amygdalina - Black Peppermint (Tasmania) A small to medium tree, widely distributed in Tasmania but not found on the mainland.  The bark is grey and fibrous on the trunk and larger branches, but sometimes salmon pink to white on smaller branches above.  It is otherwise much like E. pulchella (linearis), to which it is closely related.  Both juvenile and adult leaves are narrow and pointed, and they are a bit wider than those of E. pulchella.  It grows throughout a wide range of elevations in Tasmania and established trees have tolerated 10°F.  Hardier provenances of this species should be tried throughout zone 8.  Tolerates dry conditions if not too hot.  Moderate growth rate.  6 to 16°F.
Photos of Eucalyptus amygdalina

Eucalyptus andrewsii - New England Blackbutt, New England Peppermint (northeast New South Wales, southeast Queensland) Tall tree allied to E. consideniana.  Can be slow-growing in cool climates.  Ssp. campanulata - Stringybark Peppermint exists.  10 to 17°F.

Eucalyptus angophoroides - Apple-topped Box  Allied to E. bridgesiana, perhaps slightly less hardy and with greener, less attractive juvenile leaves.  This tree does not grow at exceptionally high elevations, but as a close relative of E. dunnii it may have considerable vestigial hardiness.  The rough bark can be flaky or fibrous.  It may be able to tolerate some degree of poor soil drainage.  Worth trying in zone 8b.  Drought tolerant.  Probably hardy to about 10 to 16°F.

Eucalyptus apiculata - Narrow-leaved Mallee Ash, Narrow-leaved Mountain Mallee (Blue Mountains, New South Wales) A rare and beautiful mallee or small tree that should prove reasonably hardy.  Its beauty lies particularly in its bark which is smooth and can be white, grey, and grey-green.  The leaves are thick, shining and green.  Related to E. stricta and likewise a very beautiful species.  It has withstood 10°F in New Zealand, but needs well-drained soils to thrive.  It is not fast growing and often sends up new stems from the base.  Its beauty makes it worth a trial throughout zone 8.  6 to 16°F.
Photos of Eucalyptus apiculata

Eucalyptus approximans - Barren Mountain Mallee, Bellfruited Ash (limited distribution in New South Wales, southern Queensland) A mallee of moderate growth that may achieve the size of a small tree to 35' or more in sheltered areas.  Juvenile and adult leaves are shiny and green; smooth bark is usually light gray.  In nature it frequently grows in large clumps, and demands excellent drainage.  Two subspecies exist.  It should be tried throughout zone 8 and perhaps in colder areas.  4 to 14°F.
Photos of Eucalyptus approximans

Eucalyptus aquatica - Mountain Swamp Gum Forms thickets in swamps and on edges of lakes.  A recent classification and little information is available about it.  Possibly hardy to the single digits F.

Eucalyptus aromaphloia - Scent Bark, Creswick Applebox As the name suggests, a key interest of this species is its scented bark.  Very fast growing.  8 to 15°F.
Photos of Eucalyptus aromaphloia