She is probably best known for the Cranberries song "Linger", but I will always remember her best for a few other songs--"Ode To My Family", "Dreams", "Free To Decide", and last but not least, "Zombie."
The Cranberries, her band, were a group whom I "accidentally" saw for the first time when they opened for Pearl Jam at Purdue's Elliott Hall of Music way back in, what, must have been 1994? No one had ever heard of them, but I thought, Man, these guys are good. And then, luckily, they exploded onto the scene.
Here's a tribute to O'Riordan, another one lost to the great beyond.