Dragon games -
DragonStrike -- Dragon flight simulator from 1990 that uses the D&D Krynn setting and takes place during the War of the Lance. The player character is a human knight riding on a dragon where your weapons are your dragon's breath and your lance. This game is pretty much vaporware in that you can play it online, but there's nowhere to obtain it if you don't already have it.
Community Wishlist entries for DragonStrike
https://www.gog.com/wishlist/games/buck_rogers_25th_century_parts_i_ii_ssi_add_dragonstrike_ssi https://www.gog.com/wishlist/games/dragonstrike Balrum - There are three dragon NPCs in this game, one of which shows up in the opening intro. Although they are significant, your meetings with them are short. Going into more details is heavy on spoilers.
Neverwinter Nights - Chapter three of the original campaign involves dragon eggs being stolen and as a result, there's encounters with three dragons: Akulatraxas (female, green), Gorgotha (female gold) and Klauth (male red.) The two female dragons want you to do whatever is necessary to make Klauth stop. There is another section of chapter three that involves a white dragon. Shadows of Undrentide has a white dragon, Tymofarrar, in the first chapter who is the master of the Deekin the Kobold bard. Wyvern Crown of Cormyr also has a dragon, Wyvernvapor, that you encounter briefly.
Dragons can show up elsewhere, such as randomly generated enemies in Infinite Dungeons. The ones that I specifically mentioned are all NPCs that you will have conversations with.