So, to sum up the replies, Flexor, you haven't missed much. You are free, and indeed will probably retain your sanity longer if you do, to ignore any Dragonlance novel not written by Weiss/Hickman. That's pretty much everything you haven't read with the following exceptions:
* The Second Generation (A collection of short stories written by Weiss/Hickman that appeared in various and sundry anthologies after the Twins trilogy) -- Tanin, Palin and Sturm are all the sons of Caramon, and they go on various adventures together, sometimes with Tas, all of which are relevant to the next book.
* Dragons of Summer Flame -- Palin, Tas, and friends must stop Chaos from destroying the world. They do, but the world is shattered, with severe side effects. Weiss/Hickman essentially washed their hands of the entire setting with this book, all at TSR's behest, which at least Tracey took personally. IIRC, they never published another thing under TSR till WotC took over.
* various "5th Age" crap that you can safely ignore -- Weiss/Hickman were out of the picture and had no control over the world, which the authors TSR put on the project essentially wrecked even further than DoSF did.
* Dragons of a Fallen Sun (First in the new War of Souls trilogy) -- Tasslehoff comes into the 5th Age world from the past using the device of time journeying, which he used right before the end of Dragons of Summer Flame. Nobody believes his outlandish tale, of course. You'll have to read the book to find out.
* Dragons of a Lost Star (Book two of the War of Souls) -- I won't tell you a thing about this book, it's too damn good! Or bad. Depends on your POV, I suppose.
* Dragons of a Vanished Moon (Book three of the War of Souls) -- Beats me, it's not gonna be published until June!!!
Oh, and for those of you who, like me, hate all non-Weiss/Hickman Dragonlance novelists, I found this funnly little linky... it's the Dragonlance Author's guide to naming a new character.
http://www.dragonlanceunderground.com/features/authorguide.html