The visionary leader
Captain Jean-Luc Picard always promotes a clear vision of what Starfleet is all about. He motivates his crew members to be the best they can be can empowers them with the knowledge they need to get out there and make it so.
Picard is leading at a time when Federation ideologies and practices have matured. In dealing with threats like the Borg and complex relationships with traditional enemies like the Klingons and Romulans, he provides excellent insight. Visionary leaders are great for times when a new direction is needed.
The coaching leader
Captain Jonathan Archer is definitely a coaching leader. He's got to be, as the captain in command of the first Starfleet starship. Archer helps his crew members recognize their strengths and weaknesses. He also forms close connections with his team, even coming to an understanding with his Vulcan first officer T'Pol, whom he initially had a contentious relationship with.
Like some coaching leaders, his style can come across as micromanagement sometimes — chronologically, Archer is the first captain to start accompanying landing crews on potentially dangerous missions. Still, all in all, his methods help lay the groundwork for Starfleet's long-term capabilities.
The affiliative leader
Captain Kathryn Janeway is a classic affiliative leader. She's all about creating harmony within her organization and healing rifts between different groups.
She demonstrates this by bringing together her crew and the rebel Maquis faction at the start of the series. Janeway even leads her Voyager team to band together with adversaries such as the Borg and Species 8472.
The democratic leader
Captain Benjamin Sisko starts out the series as a Lieutenant Commander, the Starfleet officer in charge of the Bajoran-controlled Deep Space Nine.
His no-nonsense approach to things most closely reflects the democratic style of leadership. Sisko values input from his colleagues and is always able to hear the good news and the bad news.
This style works well in the many uncertain situations he faces, as he has to deal with everyone from the Provision Government, to the Maquis, to the Dominion.
The pace-setting leader
Captain James Tiberius Kirk is definitely a commander that leads by example.
In almost every episode, he's running around exploring alien planets with his team, red-shirts and all (squad goals). He's out there fighting the Gorn, getting split in two by the transporter, falling in love with pacifistic social workers, and getting into all sorts of highly illogical trouble.
He's still a highly effective leader. Kirk challenges his crew — especially Scotty, whose protestations about diverting power to the ship's shields and other functions are typically ignored.
Kirk's all about hands-on leadership. And he always expects his crew to do their best and know how to find that "third option" when dealing with problems.
The commanding leader
Klingon starships tend to be what you might call hostile work environments.
When your Klingon leader issues an order, you either obey, get killed, or murder the commander and seize control for yourself.
This powerful (albeit bloody) approach definitely calls the commanding leadership style to mind.
One Klingon proverb in Benjamin Bonetti's"Quotes to Remember" sums up their view of a good commander: "A leader is judged not by the length of his reign but by the decisions he makes."
Maybe that's because the life expectancy of Klingon leaders probably tend to really vary.
While forcefulness and demanding full team compliance may be valuable during times of crisis, I, for one, definitely couldn't handle working on a Klingon vessel.