How did the fall of the Roman Empire (western, cir. 476 CE) affect those living in northern/northeastern Europe? Did the end of the threat of Roman legions lead to more peaceful lives for the inhabitants, increased commerce, development, etc?
The collapse of Roman authority in the west coincided with a number of larger trends that were already working their way through much of the area but were brought to a head in the death throes of the Roman state. Among these trends were economic de-specialization (and contraction) and political de-centralization. Life for those living in the aftermath of Roman collapse was not necessarily more peaceful or more prosperous though, even with the lack of an overbearing military government and the legions themselves gone. However this is partly due to a misunderstanding about how the legions and the border regions more broadly operated.
The Roman empire was an economic juggernaut of the ancient world, and even the marginal lands of the Empire, which Northern Europe certainly was, derived economic benefits from the presence of the empire, and its legions. Legions after all were not just armies on a map that existed to fight and lock down the border of the empire, they also were economic forces of their own. Landowning soldiers (and retirees), families of the soldiers, tradesmen and merchants who catered to the military, on top of the normal administration and tax infrastructure of the area all contributed to an economic system that was far and away more developed and specialized than the non-Roman areas.
This however extended into the non-Roman territories as well. Merchants, trade routes, warbands, trade goods, and money flowed relatively easy across the border of the Roman world into the rest of Northern Europe. This allowed for the development of proto-states in the interior of Germania that thrived off of trade with the Roman world, especially for luxury goods such as wine, jewelry, weapons and armor, and other trade goods, that they exchanged for goods in Germania such as slaves, amber, and furs. Many burials and grave goods from Northern Europe show how far the empire's trade connections reached, into Scandinavia, and many men saw service in the Roman legion, as evidence by the presence of Roman military goods in burials.
Once the Roman legions withdrew and the Roman state started to fall apart, this system collapsed on itself. The absence of Roman merchants and services to cater to the legions meant that large parts of the economy of Northern Europe almost disappeared. In Britain this collapse brought about the total abandonment of urban life as a whole, and a transition to an almost entirely rural lifestyle. We can trace this through the changes in material culture as well. Trade goods from across the empire, such as African pottery, start to rapidly dry up in the archaeological record, indicating a decline in long distance trade. The shift to rural living also indicates a shift back to agrarian economies (moreso than they already were) that did not produce specialized or manufactured goods for foreign export, but rather subsistence farming and limited/local trade that operated around the North Sea and along rivers, not into and around the Mediterranean world.
The collapse of Roman state power also changed the political landscape of the area as well. Many new polities rose up, with varying degrees of continuity to Roman times. Many of the new polities such as the Frankish, Ostrogothic, Visigothic, and Burgundian kingdoms of Western Europe attempted to maintain Roman institutions, this includes both infrastructure such as roads, aqueducts, and bathing systems, as well as administrative systems such as tax collection, the Senate, and civic involvement.
They were not entirely successful at this. While systems such as the baths and aqueducts often survived in the limited surviving urban areas of Western/Northern Europe, these other systems fell apart after the Roman empire disintegrated. Indeed the collapse of Roman financial institutions were probably the biggest influence on Northern/Western Europe for the next several centuries. The lack of financial resources, that was the limiting factor on the capabilities of these polities such as the barbarian kingdoms, they were unable to exert economic power over their own territories. Tax revenues especially were vital for the functioning of the late Roman state and the ability to collect taxes fell off a cliff following Roman collapse.
The new polities also did not get along with each other, and even beneath the state on state violence, the Franks kicked the Visigoths out of Gaul, the Burgundians fought the Franks, the Lombards and Ostrogoths fought, the Byzantines meddled, and so on and so forth. Now England may have been a limited exception this this pattern of state violence. Robin Fleming examines the evidence of the post-Roman period and find the evidence of endemic violence and warfare....wanting. But even allowing for this potential exception, the endemic violence, not only between state actors, but also between rival warlords, and the nascent and growing nobility of these areas, did not disappear. The Roman legions were no longer around to scorch the earth of Germania and Frisia, but the rival lords of the land still carried out raids and violence on each other, and the populations they ruled. Indeed over time, these areas would also be laid open to raids and violence from new corners of the map! The Arab invasions of the 8th century brought raiding parties to the center of France, Viking raids of the 8-10th century did likewise, the Irish and Picts raided into lowland Britain, and the Magyars raided deep into Central Europe. These kinds of movements were not unprecedented before the collapse of the Romans, but the ability of the new states to resist them were far less than Roman resilience in the face of outside threats.
So in short, the collapse of Roman power in Western/Northern Europe was a mixed bag for many of the people living there. The onerous taxation burdens of the empire were gone, and the de-urbanization of the lands probably actually raised some standards of life (Antique and Medieval cities were massive population sinks with far larger amounts of deaths from disease and squalor than births), but this was coupled with economic collapse and internecine warfare.