Well, I think we have to start off with the caveat that "positive influences" is a subjective term, and what we consider to be positive is often informed by the culture we live in.
Very frequently, ideas of "modernity" expressed as resembling current Western societies and economies is regarded as a positive things, by Westerners. Of course, there are critics within and outside of the West (or the Global North, or the First World, however you want to call it) that would dispute the idea that "West is Best" and other societies are improved by conforming to European norms. You cited democracy as an example of a positive influence. Of course, Prime Minister Lee Kuan Yew of Singapore often criticized Western democracies for becoming preoccupied by trivialities, and promoted the idea that Singapore's economic growth occurred because of he promoted discipline (or pragmatic authoritarianism) rather than democracy.
With those things said, there were some processes that occurred during the era of Colonialism/Imperialism that made them resemble European or American society. (For simplicity's sake, I will mostly confine my observations to the 1870's to the 1960s, and heavily focus on Africa where I am most familiar)
Colonial regimes did cause the construction of railroads in areas of Africa and India for the linking of plantations, forests, mines, or other areas of exploitable resources to ports for export. Those railroads continue to be used for transportation of goods and people today.
The era from 1870 to 1960 saw the introduction of European medical knowledge and construction of European style hospitals in Africa. At independence, the medical services of many of these African states were built on this colonial era medical infrastructure.
Missionary societies were responsible for publishing the first written works in many African languages, and establishing schools to teach literacy. Almost invariably, the first book published in a language would be copies of the Bible.
This era did also see the construction of several universities. Examples only from the British colonies in Africa include the University of Makerere in Uganda, the University College of Ibadan in Nigeria, and the University of Dar Es Salaam in Tanzania. Other colonial powers like France or Portugal would bring students from important African families in their colonies to study in Paris or Lisbon.
Of course, it bears mentioning that this access to higher education, particularly in the case of France, was seconded to the idea of a "Civilizing Mission". That is, by bringing people like Leopold Sedar Senghor to Paris to study, he could be "civilized" by adopting French language, culture and ideas; and would return to serve the colonial bureaucracy (though never at the highest levels).
This leads to the next question, "was colonialism worth it to African states?".
I believe most Africanist historians would answer that question with a "no". That is not to say that those specific pieces of infrastructure should be rejected. Rather, the violence, degradation, and exploitation inherent in Colonialism were negative factors that outweigh those benefits.
Additionally, the introduction of each of the influences I listed above can't be seen as straightforward positives. The construction of the railroads was accomplished through the widespread use of forced labor. The expanded opportunities for transportation led to dramatic spread of diseases like Influenza in 1919, or Smallpox during World War 2 mobilization. And fundamentally, the routes of the railroads were not designed to meet the needs of the local populations, but with the goal of carrying resources out of Africa to be used in Europe or America.
University education required students adopt the language of the occupying power, and by keeping local African languages outside of education, enforced a dynamic where speaking a European language is seen as "cultured, modern, intellectual" while speaking a local language is seen as "backwards". Specifically in the case of France, university education exposed the contradiction between the promise of full acceptance for all evolue Africans with the reality of continued discrimination.
Finally, I think it is a trap to think that because these influences occurred during the period of Colonialism/Imperialism, that colonialism was the only way to introduce them. Meiji era Japan and Ethiopia under Yohannes IV, Menelik II and Haile Selassie are examples of states that incorporated European institutions and technologies without being subjected to colonial regimes. (It should be noted that both Japan and Ethiopia embarked on their own Empire-building programs after 1870).
As the one being colonized, or doing the colonizing?
There is no "one" form of Colonialism. Colonialism in British Australia, was very different from Colonialism in French Indochina, which in turn was very different from Qing colonization of the North West.
And that is only if we are talking about 19th century colonialism, since colonialism, is as old as the state, with Phoenicians and Hellene City-states setting up colonies across the Mediterranean to relieve population pressure on the land.
While this is not a very specific question, here are some things that might objectively be considered beneficial that occurred with some kind of frequency in European colonies:
Not all of these occurred in every colony and for every group within a designated colony, or in ways that were immediately or directly beneficial to the natives, but it should get you on the right track for some of the scenarios.