My go at a Vikings list:
1)
Ragnar loðbrók /
Ragnar Lodbrok / Ragnar Shaggy-breeches (quintessential semi-legendary Viking king)
2)
Knútr inn ríki /
Cnut the Great (united the crowns of England, Denmark, and Norway into a "North Sea Empire")
3)
Haraldr hárfagri /
Harald Fairhair (united Norway, gained a reputation for harshness that drove people to settle Iceland)
4)
Sveinn tjúguskegg / Sweyn/
Sven Forkbeard (ambitious King of Denmark, ruled Norway by proxy and England briefly before his death)
5)
Haraldr harðráði /
Harald Hardrada / Harald Hard-ruler (last great Viking king; good King of Norway, less good at claiming other kingdoms)
6)
Hrøríkr /
Rurik (supposedly invited by Slavs to rule over them in Novgorod; founder of the long-lasting Rurikid Dynasty)
7)
Haraldr blátönn /
Harald Bluetooth (King of Denmark, converted the country to Christianity, ousted by his son)
8)
Óláfr skautkonungr /
Olof Skötkonung / Olaf the Swede (king of both Svealand and Götaland in Sweden; first Christian Swedish king)
9)
Óláfr Tryggvason /
Olaf Tryggvason (short-lived reign spent violently converting Norway to Christianity)
10)
Auðr djúpúðga /
Aud the Deep-Minded (Norse-Gaelic settler of Iceland; most respected chieftess in Iceland's history)
11)
Þorgeirr Ljósvetningagoði / Thorgeir Ljosvetningagodi (Lawspeaker of Iceland who made the controversial decision to convert to Christianity)
12)
Eiríkr rauði /
Erik the Red (outlawed from Iceland for murder, founds/leads the Greenland colony; tricks people into joining him with the name)
13)
Þorfinnr karlsefni / Thorfinn
Karlsefni (tried to establish a colony in Vinland... this didn't work out very well)
14)
Eiríkr blóðøx /
Erik Bloodaxe (only briefly King of Norway, quickly fell out of favor for his despotic tendencies; later career in Britain also fraught)
15)
Blót-Sveinn /
Blot-Sweyn/
Sven / Sven the Sacrificer (propped up as King of Sweden in an unsuccessful pagan revolt against Inge the Elder)
16)
Fjölnir / Fjolne (though apparently a decent ruler, this legendary king is most famous for drowning in a vat of mead)
Obviously I stuck to the Viking Age, since the civilization is the Vikings and there's quite enough material in medieval Norse written sources to fully occupy the list. The UU, UB, UP, and UHV are all pretty specific to the Viking Age, so I figured that would be the preference.
My goal was to represent as many corners of the Viking world as possible - Denmark, Sweden, Norway, Iceland, Greenland, Vinland, British Isles, Rus', etc. If/when Sweden is introduced in the future, that list should probably restrict itself to Swedish rulers after the Swedish start date.
Bolded are the versions of the names I would probably go with, but that's just personal preference.
I'd be interested to hear any critiques! A lot on here is definitely debatable, particularly given the (sometimes conflicting) sources that we have.