Among airlines I know about, Cathay Pacific, Southwest, and Alaska all have it so that the same flight number means that you are scheduled to stay on the same airplane. On United and Delta, the same flight number is no guarantee that you are scheduled to stay on the same aircraft, and in most cases, you will not and have to make a connection (or miss the connection).
On AA, the DFW - ORD - LHR / LHR - ORD - DFW flight is all on the same aircraft (back in the secret-upgrade-strategy days, I was able to fly in AA's flagship F suites on flights between DFW and ORD on this equipment); AFAIK, the DFW - RDU - LGW / LGW - RDU - DFW is as well.
