An interesting fact about Massachusetts, the town of Rehoboth was once in consideration for the capital of the state. As a town with a population of 11,608 it makes no sense now... but at the time, it was much bigger - in population and in area. Rehoboth's territory included present-day cities of Attleboro, East Providence RI, most of Pawtucket RI, and others.
Similarly, Columbus has grown in size over time and eclipsed the former bigger cities of Cleveland and Cincinnati.
I started in the NE and zigzagged north and south. Albany - Annapolis - Atlanta - Jackson - Austin - Lansing - Oklahoma City - Jefferson City - Bismarck - Boise - Denver - Salt Lake City - Sacramento - Honolulu - Juneau - Olympia - Phoenix. Thank God it accepted "pheonix" for the last one.
Off the top of my head, nations in which this has clearly played out include Canada, Switzerland, Tanzania, Canada, Myanmar, Brazil, Pakistan, Nigeria, South Africa, and the US itself. I'm sure others can come up with many other examples even excluding countries such as India where the capital has clearly been an important city for ages even though it's not currently the largest city.