Kiwiberries are quite resistant to disease, but they are susceptible to phytophthora root rot in excessively moist soil.  Conversely, soil that dries quickly can dramatically slow growth – at least for a few years.  Although the complaint seems to be quite rare, the spotted wing drosophila (Asian fruit fly) may be a problem in regions that have a longer grow season than those typically found in the north, otherwise they don't have any significant pests either.  Hardy kiwi (Actinidia arguta) occasionally experience one relatively serious issue, though.  Productivity may begin to fade at some point, or fail to produce well from the start, but a heavy pruning can solve this problem. 

Kiwiberries perform well if they are grown fairly close to the ocean or a great lake.  Most other places in North America have a very unstable climate, so their fruiting shoots often suffer from frost damage.  However, damage strictly to young leaves can be insignificant.  Some varieties developed in the south may awaken much later than most, but they are rather new and they are not kiwiberries.  They belong to the species 'Actinidia chinensis'. 

Hardy kiwi are borderline invasive and may take 4-7 years to produce – with the primary exception being Issai, which can fruit very quickly.  Arctic kiwi are easier to control and begin to produce much sooner, but their leaves are fairly sensitive and may require some shade in climates that are quite hot.  While there are some minor exceptions, a male vine is required for production, regardless of species.

Hardy Kiwi: Actinidia arguta

Anna

🔍
Originated in Russia
Alias
• Ananasnaya, Annasnaya
Zone
• 4b
Ripens
🥝
• late
Color
• green skin with a purple-red blush
Fruit
• small size
Yield
• highly productive

Out of the 6+ varieties I have seen, Anna develops the most attractive fall colors in my warm-summer humid continental (Dfb) climate.

Chang Bai

🔍
Seedling of Qui.  Selected in China near the border of North Korea.
Zone
• 4b
Color
• green skin
Fruit
• medium-small size
• flat pumpkin shape

I have not heard of any reports from other people, but in my experience, the quality of Chang Bai has been quite variable.  Some berries are very good while others are quite unpleasant, which is something I have experienced for three or four years in a row now.  However, the vine has a different aesthetic than the other hardy kiwi I have seen, and I think it is quite nice.

Cherry Bomb

🔍
Zone
• 4b
Color
• red skin

Cherry Bomb supposedly develops a cherry-like flavor.  Unfortunately, no one talks about this variety, so I haven't seen any reports that have confirmed or denied this claim.

Cordifolia

🔍
Zone
• 4b
• low chill
Color
• dark green skin
Fruit
• relatively sweet?

Cordifolia may also be referred to as 'Meyer's Cordifolia' to avoid confusion with another variety that is now being referred to as 'Early Cordifolia', but I don't know the full story.

Dumbarton Oaks

🔍
Selected in Georgetown, Washington D.C.
Zone
• 4b
Ripens
🥝
• early-mid
• ~3 to 4 weeks before Anna
Color
• light green skin

Dumbarton Oaks should be the second earliest ripening hardy kiwi variety, which could be important for those with short grow seasons (Anna ripens throughout October in my Dfb climate).  Fifty Five should ripen about two weeks earlier than Dumbarton Oaks, but this, of course, may depend on which locations are being compared.

Fifty Five

🔍
Zone
• 4b
Ripens
🥝
• early
• roughly 6 weeks before Anna

Fifty Five appears to ripen much earlier than the other hardy kiwi varieties available.

Fortyniner

🔍
Developed in Chico, California.
Zone
• 4b
Ripens
🥝
• mid-late
• somewhere between Dumbarton Oaks and Anna

Fortyniner might be the same variety as 74-49.

Geneva

🔍
Selected in Geneva, New York.
Zone
• 4b
Ripens
🥝
• mid-late?
• somewhere between Dumbarton Oaks and Anna

Hardy Red

🔍
Zone
• 4b
Color
• red skin

Hardy Red has supposedly done well in taste tests according to nurseries.  I have not seen any results or heard about this variety elsewhere, though.

Issai

🔍
Originated in Japan
Zone
• 4b
• 300 chill hours
Flowers
• partially self-fertile (parthenocarpy)
Ripens
🥝
•    ◦ precocious
Color
• green skin

Issai grows less vigorously and begins to produce much sooner than most arguta varieties.  It is also partially self-fertile, which is unique for a kiwi, but this trait appears to be quite weak, so you should consider relying on a male for pollination.

Jumbo

🔍
Originated in Italy
Zone
• 4b
Fruit
• medium-small size

Jumbo, which is probably the same variety as MSU (Michigan State), produces large berries for a hardy kiwi, roughly two to three times the size of Anna. 

I was only able to sample a few berries from MSU, but I thought they were pretty good and different enough from Anna to keep my interest.

Meader Male

🔍
Zone
• 4b (4a)

One report claims that their Meader Male kiwi vine survived temperatures as low as -28F (-33.3C). 

Natasha

🔍
Originated in Vladivostok, Russia.
Zone
• 3b

Ogden Point

🔍
Zone
• 4b

Prolific

🔍
Zone
• 4b
Flowers
• partially self-fertile (parthenocarpy)

Rossana

🔍
Selected in Italy
Zone
• 3b

Tatyana

🔍
Zone
• 3b
Color
• light green skin

Hybrid Kiwi: Actinidia hybr.

Flowercloud Male

🔍
A. arguta x A. kolomikta
Zone
• 4b?     ◦ lower

Flowercloud may begin to flower as soon as the year after planting, but it might bloom too early to pollinate female hardy kiwi vines in some climates due to its hybrid parentage.  

Ken's Red

🔍
A. arguta x A. melanandra.  Originated in New Zealand.
Zone
• 4b?     ◦ higher
• low chill
Ripens
🥝
• late?
• somewhat biennial?
Color
• red skin

Red Princess

🔍
Cordifolia (A. arguta) x A. melanandra.  Originated in New Zealand.
Zone
• 4b?     ◦ higher
Color
• red skin

Arctic Kiwi: Actinidia kolomikta

Emerald

🔍
Zone
• 3a
Color
• light green skin

Frost

🔍
Zone
• 3a
Ripens
🥝
• early? (early-mid)

Frost ripens earlier than most Kolomikta varieties.

Hero

🔍
Selected from the wild near Vladivostock, Russia (Far East).
Alias
• Dostoynaya
Zone
• 3a
Color
• light green skin

'Hero' has an unconfirmed report about being partially self-fertile.

Pasha Male

🔍
Zone
• 3a

The leaves of Pasha develop white and pink colors.  If 'Pasha Male' is similar to those sold under the name of 'Arctic Beauty Male', the colors are amplified by full sun exposure.

Red Beauty

🔍
Zone
• 3a

September Sun

🔍
Originated in Russia
Alias
• Sentyabraskaya
Zone
• 3a
Ripens
🥝
• mid?

September Sun was once the only female in the US that produced ornamental leaves, similar to that of the male arctic kiwi vines, but new varieties with the same trait are starting to circulate the country.

Viktor

🔍
Selected from the wild north of Vladivostok, Russia.
Zone
• 3a

Viktor produces larger berries than most kolomikta varieties.

Golden Kiwi: Actinidia chinensis

Golden Kiwi often ripen 1 to 2 months before Fuzzy Kiwi (Actinidia deliciosa) and a few varieties have been developed to awaken from dormancy much later, which generally makes them a more appropriate option. However, these varieties may be difficult to obtain at this time.

AU Golden Dragon

🔍
Zone
• 7 (6b)
• 800 chill hours
Ripens
🥝
• late?
• mid-late August in central Alabama
Color
• yellow-green flesh
Fruit
• large-size, 89 g/fruit

Golden Dragon can hang on the vine for roughly a month after maturing, but the fruit will become very soft.  This may be typical for many chinensis and deliciosa varieties, and they may be able to hang much longer than that, provided it doesn't get too cold.  AU Golden Dragon is unlike the other two listed here in that it does not awaken from dormancy late, so it should not be paired with AU Golden Tiger Male.

AU Golden Sunshine

🔍
Selected in Alabama from material that originated in Chongyang County of China (Hubei Province).
Zone
• 7 (6b)
• 700 chill hours
Buds
• break in early April in central Alabama (later than most varieties from any species)
Blooms
💮
• late    ◦ mid-late April in central Alabama
Ripens
🥝
• very late?
• matures mid September in central Alabama
Color
• yellow flesh
Fruit
• large-size, 90 g/fruit

AU Golden Tiger Male

🔍
AU Golden Dragon x unknown male (pollination occured in China).  Selected in Auburn, Alabama.
Zone
• 7 (6b)
Buds
• break later than most (along with AU Golden Sunshine)
Blooms
💮
• late    ◦ along with AU Golden Sunshine