Trade: I would not consider it a part of the long-term impact of the Vikings. In fact, in many ways, it appears that trade was rather the “bridgehead” of the Viking attacks: frequent contacts with the people with which they traded were a good source of information about their wealth, and their weaknesses (it is striking to see how well-informed the Vikings seem to be in general: for instance, one of their most remarked attacks on continental Europe, the siege of Paris, happens in 885/6, precisely at the moment when West Francia was the most vulnerable because of the utter lack of leadership). In some cases (especially in the British islands: Dublin, York), it may be argued that the Vikings had a role in reshaping the urban landscape through their trading activities, once they had taken control of a given place. But generally, I think that it is preferable to think of trade in terms of impact on the Vikings themselves: riches they could get this way acted as a bait, and contributed to the undermining of the equilibrium of the traditional Scandinavian society.

Military conquest: there is an ongoing (and neverending) debate about the amount of violence caused by the Viking attacks. Let's just say that a “revisionnist current” (starting with the excellent work of P. Sawyer in the 60s) downplayed the actual impact of Vikings; then, more recently, historians (I cannot point to a seminal article or research in particular, but Alfred Smyth, 'The effect of Scandinavian raiders on the English and Irish churches: a preliminary reassessment' is worth looking at) have underlined that the violence of warfare had been downplayed beyond reason. [1]

— The revisionists/maximalists think that we rashly overestimate their impact because of the ecclesiastical bias of our sources. Monasteries and churches, as important deposits of wealth (that the pagan Vikings had no reason of holding in high regard) that went mostly undefended, were prime targets for plunderers. However, they say, Vikings had no reason of targeting peasants, who did not own important sources of movable wealth at that time (i.e. precious metals, mainly).

— The traditionnalists (who are actually “revising” the revisionist paradigm, which had become predominant) underline that roaming bands of plundering barbarians can hardly have left untouched the countryside, and that constant warfare during decades in certain zones (coastal areas, main rivers) must have been a major source of unrest.

Apart from the question of violence, it is obvious that the Vikings served as catalysts of political change in the areas that came under attack. To take just an important example, the great-grandfather of Hugh Capet (who was to become king of West Francia in 987, effectively ending Carolingian rule in Europe) Robert the Strong, gained his fame by his success against the Vikings, and by his heroic end at their hand at Brissarthe in 866. In Anglo-Saxon England, the changes brought by their arrival were arguably even greater: though the importance of Wessex had been growing for a while (just like the influence of the aristocracy was already becoming greater in Francia), the Scandinavian threat was arguably very important in the redefinition of the political equilibrum in England.

Rule: the Vikings undoubtedly contributed to the creation of major players in the political game, by creating state-like entities in areas that were previously tribal (a good example of this, though our knowledge of the process is unfortunately quite poor, is the creation of Rus' on the border of the steppe world). However, their positive contribution to local culture is less clear: most of the time, they were absorbed by the people they ruled. In Normandy, there was hardly any Viking specificity by the 11th century, and apart from the ducal line, it is hard to point out any important lineage that was clearly of Viking origin; in Rus', the Swede aristocracy adopted Slave culture (in fact, even the contribution of the Turkish nomads is arguably more important in the identity of early Rus' than Scandinavia); etc. The exception may be Great Britain, where evidence of substantial settlement (through archeology, topography and linguistics — for instance the apparition of “they” in the English language) is stronger than elsewhere. Even sources like Beowulf (if we accept a late date for the poem) prove the influence of Scandinavian culture on England.

[1] Interestingly, the study of Germanic migrations has undergone exactly the same process; it has been suggested that the euphemisation of warfare was due to the period of European peace after the Second World War.