The Koopa Cruiser was Bowser's unarmed transport/dropship in Mario & Luigi: Superstar Saga and Mario & Luigi: Partners in Time. It is used to transfer troops, sentries, and high ranking government officials like the Koopalings or the King. An early version of this that was designed by Baby Bowser appeared in Mario & Luigi: Partners in Time but was demoted in later classes to medium transports most likely that because of how the early Koopa Cruisers where only armed with a single rear cannon, and where noticeably small.
Mario & Luigi: Superstar Saga
In Mario & Luigi: Superstar Saga, Bowser, Mario, and Luigi used it to get to the Beanbean Kingdom to find Cackletta and Fawful. The latter two found the former two and, after Fawful was defeated by the Mario Bros., destroyed the ship. It was later (slightly) repaired, but under the sole use of Bowletta and Fawful.
Mario & Luigi: Partners in Time
In Mario & Luigi: Partners in Time, Baby Bowser called on Kamek to bring him the Koopa Cruiser to get him, Baby Mario, Baby Luigi, and Baby Peach out of Peach's Castle while it was under attack by the Shroobs. Later on, he used it to kill off some of the Shroobs so the Baby Bros. could reach their adult counterparts: Mario and Luigi. It was attacked by the Shroobs and crash-landed into Baby Bowser's Castle.