This is a direct excerpt from staroceanuniverse.com
The games begin as early as Space Date 10 (The Last Hope) and have extended to as far as Space Date 772 (Till the End of Time). Check below for a summary of the time line for all of the Star Ocean titles released to date, in Space Date order, not game release order.
Star Ocean: The Last Hope: 0010 SD
Star Ocean: First Departure (past events): 0046 SD
Star Ocean: First Departure: 0346 SD
Star Ocean: Second Evolution: 0366 SD
Star Ocean: Blue Sphere: 0368 SD
Star Ocean: Till the End of Time: 0772 SD
Star Ocean: Role Play: 1272 SD
As a general rule (Till the End of Time aside) the time line of each title has allowed them to intertwine with each other somewhat, where characters or relatives to the characters of the games has made appearances throughout. With the exception of a few characters, such as the Welch who somehow has managed to appear in every major Star Ocean title to date thanks to the PSP remakes.
Background Information
While the games take place in a futuristic environment it's not limited to out of this world, fancy technology. Only Earth and some other planets have such advanced technology, while other worlds, such as Elicoor II from Till the End of Time is still developed as much as Earth in the 17th century. Thankfully however many of the Federation nations (a bunch of nations that adhere to a number of space rulings), including Earth has an all important ruling known as the "Underdeveloped Planet Preservation Pact", otherwise abbreviated as the UP3. This very ruling prohibits those from more advanced worlds from engaging with lessor developed worlds to allow them to thrive under their own ways without outside interference. Sadly though not all nations are part of the Federation, much less agree with the ruling and at times this will be one of the many issues you face throughout your games, particularly considering under what circumstances is it reasonable to breach these rulings for the betterment of such worlds.
The Star Ocean series contains a number of typical RPG elements, fight to gain experience and Fol (the type of currency for the Star Ocean titles), level up, go shopping, etc. But a few of those more unique to the series are shown below.