Other European nations did colonize North America. The other major colonial powers at the time were the Spanish, French, and the Dutch. Each of these countries had possessions in North America. The Spanish had colonies in Florida and Mexico (including parts of what is now the southwestern US). The French had several colonies around the Mississippi, including New Orleans. The Dutch held much of the land which later became the Middle Colonies. The English ended up taking the Dutch colonies, but the Spanish and French colonies lingered until after the founding of America. The US purchased France's colonial possessions in the Louisiana Purchase and took Florida from Spain by treaty in the 1820s. No war was fought. Florida had become a burden to a declining Spain and the territory was ceded to the US because Americans had settled in Florida in sufficient numbers to prevent policing by the Spanish. The Southwestern US was taken from Mexico during the Mexican-American War, after Mexico had gained its independence from Spain.

Which countries might have colonized America but didn't?

The answer to this question depends on what you mean by "America". You could be referring to North America, North and South America, or the United States of America. In the 15th century, England was the most prominent colonizer of what is now the United States. France had begun colonizing modern-day Canada, while Spain was the colonizing force in modern-day Mexico. The reason for using the language of "modern-day" is that this continent had many different names by different Indigenous tribes, and this land is only now known as the United States, Canada, and Mexico after brutal and genocidal colonization.

Spain could have certainly also been involved in colonizing the United States, and did have, for a period of time, colonial control over the land now known as Florida. However, Spain and Portugal had their sights on controlling Mexico, Central America, and South America as well as regions of Africa. Italy did certainly have the navigational power in the 15th century to travel to the Americas, as did the Dutch. The Dutch were much more involved in colonization of the East Indies, while Italy was much more involved in later colonization of regions of Africa. Germany and Belgium also became colonial powers later on during the 19th century in Africa, but they may have been able to be involved in the colonization of the Americas.