Will Riker (Jonathan Frakes) turned down several promotions before accepting the captain's chair aboard the USS Titan at the end of the Star Trek: The Next Generation movies. Riker was much sought-after during his time as Jean-Luc Picard's number one. However, for a number of reasons, he would always turn down these potential promotions. Riker's attachment to the Enterprise and his womanizing defined the character during TNG, and his experiences presumably convinced him to grow up in Star Trek: Nemesis by marrying Deanna Troi and taking command of the USS Titan.
In Nemesis, he finally felt ready to move on from the Enterprise, and live up to the potential that many, but not all, of his senior Starfleet officers saw in him. For example, in the season 6 two-parter, "Chain of Command", Riker clashed with Captain Jellico, who had replaced Picard during a covert mission behind enemy lines. Despite Picard's admiration for Will, Jellico believed that Riker wasn't suitable for such a vaunted command position. This clearly isn't a feeling shared by the wider Starfleet organization, who offered Will Riker promotion to captain several times, and which he turned down for a variety of reasons.
The USS Drake
Prior to accepting the post on the Enterprise-D, Will Riker was offered command of the USS Drake, a light cruiser. The young commander was in demand at this time, as he'd also attracted the attention of Captain Jean-Luc Picard. Riker's time on the USS Hood was what appealed to Picard, who had read about how Trek's Will Riker had risked court-martial to protect his captain by refusing to allow him to transport into a hostile situation, putting the safety of his crew above his own reputation.
It was while on the USS Hood that Riker received the offer of commanding the Drake and the offer of being first officer aboard the Federation flagship. Riker decided that the Enterprise was a much better posting, and declined the posting on the Drake. If Riker had taken the posting on the Drake, it's likely that he wouldn't have become the legendary Starfleet officer he would later become. Riker's fellow student at the Starfleet Academy, Paul Rice took the post instead, and was killed by a sentient weapon that had wiped out the inhabitants of the planet Minos in TNG season 1, episode 20, "The Arsenal of Freedom".
The USS Aries
When its captain retired, the deep space exploration vessel, the USS Aries was in need of a new one, and Starfleet Command decided Will Riker was the ideal candidate. He was selected because of his talents as a diplomat and explorer, but Riker wasn't convinced. Given how exciting life was aboard the Enterprise and the USS Titan, it's easy to see why Will wasn't convinced by the prospect of captaining a deep space exploration vessel.
Riker eventually decided to decline the offer, deciding that the Enterprise was the best place for him. His decision to turn down a command position surprised his father Kyle, who was assigned to the Aries as a civilian tactical advisor. This decision also surprised Riker's transporter clone Thomas, when he was rescued from the planet Nervala IV, and informed of Will's many adventures in the past eight years.
The USS Melbourne
Prior to Jean-Luc Picard's assimilation into the Borg Collective and the Battle of Wolf 359, Riker was offered command of the USS Melbourne. He was conflicted about leaving the Enterprise, but his decision was made for him when the Melbourne was destroyed by the Borg at Wolf 359. During Picard's ordeal with the Borg, Riker got command of the Enterprise-D, but at the cost of Jean-Luc Picard's individuality. Riker's efforts during the battle with the Borg earned him the choice of commanding any ship in the fleet, but Riker assured his rival Commander Shelby that his career plans were up to him, serving aboard the Enterprise for another 12 years.
The USS Voyager
It's implied in Star Trek: Voyager season 2, episode 18, "Death Wish" that Riker was also offered command of the USS Voyager. In "Death Wish", Q (John de Lancie) meets Captain Kathryn Janeway (Kate Mulgrew) for the very first time, and observes that he was "betting that Riker would get this command". As "Death Wish" aired two years after the TNG finale, audiences never got to see an episode where Riker was offered command of Voyager's mission to the Badlands. As Will's transporter clone Thomas, and his colleague Ensign Ro Laren (Michelle Forbes) both betrayed Starfleet for the Maquis, he would actually be an ideal choice for the role, but clearly he turned it down.
Why Riker Finally Became Captain Of The Titan
Riker finally accepted it was time to move on from the Enterprise in Star Trek: Nemesis, and the final TNG movie ended with he and his new wife Deanna Troi transferring to their new ship. In a film that was widely criticized for not giving the TNG cast a satisfying ending, Troi and Riker's story is the only one that's actually resolved. Will Riker had always put his career ahead of his relationship with Deanna, but in accepting command of the Titan and marrying Deanna, it's clear that he's finally been able to balance his professional and personal life.
It's this decision that finally allows him to step out of the shadow of Jean-Luc Picard and become a legend in his own right, being worshiped by Brad Boimler in Star Trek: Lower Decks. Riker's time on the Titan was very dramatic, involving space battles and covert missions, bolstering his abilities. Riker's skills as a captain were so in demand that, by the time of Star Trek: Picard season 1, he was a reserve captain, deployed in times of need. One of those times is on the horizon, as Riker is called back to service by his old captain for the Star Trek: The Next Generation crew's final adventure in Picard season 3.