Dragonlance was my introduction to D&D, even though I didn't know what D&D was at the time. I received an omibus of the Chronicles as a present for my 11th birthday; it sat on my shelf for over a year before I read it. It blew my mind, and basically kickstarted my love for fantasy fiction. I loaned it to everybody I knew, and one friend started a tradition of signing their name in the page that marked the halfway point through the volume. By the time the book fell apart, it had some 20-30 signatures on it. I still have that page.
The Dragonlance Chronicles also illustrate the fallacy of some common beliefs in D&D, foremost the thought that because AD&D/2e classes weren't customizable, all fighters (to use the most egregious example) were exactly the same. The core cast of characters in the Chronicles includes mostly fighters: Flint, Sturm, Caramon, Tanis, Kitiara, Laurana, - and they couldn't be more different from one another if they tried. Dragonlance also includes some pretty complex characters, including Tanis and of course Caramon and Raistlin, whose complex motivations and personalities defy the commonly derided black-and-white morality of the setting.
Now, playing in Dragonlance as a campaign setting? More problematic. It's hard to top the War of the Lance for a story, and unfortunately the setting - at least on Ansalon - seems to encourage stories like that one. For my money, the better Dragonlance campaign setting is Taladas. Almost all the cool stuff, almost none of the baggage.