I’ve had my MacBook for just over three years (just past AppleCare, alas), but recently the trackpad had been acting up. I couldn’t get it to click and drag at all. Opening up the case showed me that the battery was getting a bit, well, tubby — something that apparently happens as Lithium Ion batteries age.
I finally ordered a new one, and it came today. It’s nearly 50% slimmer, and sits flat on the table, unlike the old battery. My trackpad works perfectly again.