We only recently acquired this car, but a few things have gone wrong already:
The oil sensor light kept going on.
The Exhaust system began to make the car sound much more powerful and loud than a Corolla should.
A brake rotor cracked.
First off, I have to say this car has never left me stranded, although some things have gone wrong, nothing has ever been such a necessity that I've needed a tow.
I do also have to say that the brake rotor was my fault, although it happened on its own. I had run the car into a curb a month or so beforehand late at night in a snowstorm. At the time the mechanic told me it was simply a bent rim (which was cheaply replaced). However a few months later when a lady lightly rear-ended me the cracked rotor gave way.
So over all this car has been very reliable, if you could ignore the oil sensor light, and having your little car sound like a motorcycle it would not have even had to go in for repairs the first time.
The only thing I have to say is that if you are planning on buying a Corolla, get a manual transmission. The Automatic transmission Corollas are far too slow.
I highly recommend them all around, as long as you can stand how basic they are, and the small size, then they are the perfect car for anyone who just needs to get around.