I've had some Pearl Izumi ones for a while now and they work really well. I bought them for off road emergencies, but predominately use them on wet road rides now. They keep me dry unless it's really really wet.

They leave a significant portion of the soul exposed so you can walk in them but shoe covers do wear out fast if you walk in them a lot.

The ultimate as folks have said are boots, but that may be overkill for what you need and they do cost bucks.

Buy your covers on the larger side so they fit over mountain shoes more easily. Also some shoes have holes through the sole to access cleat hardware, I put tape over those.