As far as I know, Venice in the late 15th century was one of the foremost naval and commercial powers in Europe, with the massive ship-producing power of the Arsenal and it's trading network throughout the Mediterranean and Black Sea. Why did it never join Portugal and Spain and the other European powers in colonizing the New World?
After further thought, I suppose the same question can be asked about Genoa too.
Venice faced a few issues around the time of the discovery of the New World. It was just coming off a disastrous war with the Ottomans which saw large parts of its Mediterranean empire lost. Afterwards, they faced more issues with the Italian wars which were devastating for the Venetians.
Another issue which plagued the Venetians at this time is that there navy was largely comprised of oared galleys which were effective in the Mediterranean but were not good ocean-going vessels. The Venetian ability to finance new ships was also damaged with the Portuguese voyages around the Cape which broke the Venetian monopoly of the Asiatic land-based trade routes which greatly diminished Venetian profits.
Genoa was a Spanish satellite state officially in 1528 after years of difficulties so they never really were stable enough to colonize.
Venetian ships were not suited to travelling across the Atlantic. The Venetians used Galleys which were made for the very particular climactic conditions of the Mediterranean. For instance, they were incredibly shallow and not built for Atlantic waves. For instance there were a couple of galleys in the Spanish armada which sailed for England in 1588, none of them made it to the actual battle since they could not cope with the trip from the Med to the Channel. They also could only carry enough food an water for about two weeks, not nearly enough time to cross let alone get back again.
Why would they want to? The source of their wealth came from controlling the trade routes from China to Europe. They were the entrepôt by which silk and other such goods made its way to Germany. What possible economic reason could there be for going off to colonise the new world when the monetary rewards were so uncertain? Further, they did not have the money to spare. They were constantly fighting a low level war with the Otttomans in the Eastern Mediterranean and were slowly losing their holdings, Cyprus was one of the last major ones in 1570, and were enthusiastic participants in the Holy League wars that culminated in the Battle of Lepanto in 1571. All this required huge expenditure that left little room for adventuring.