Timeline 1: Reptite Timeline. In this timeline, Lavos never lands. Instead of the Humans winning the war in 65,000,000 BC, Reptites do. As a result, in the future, Dragonians, the evolved form of Reptites (as Humans are the evolved form of Neanderthals) are the dominant sentient life on Earth, and Humanity is long since extinct. Reptite civilization expands quite extensively, and they eventually create a giant biological construct they name the Dragon God, which controls natural forces. They also build a very advanced town, named Dinopolis. Around 2400 AD, due to the Time Crash, Dinopolis and the Dragon God are pulled into an alternate dimension.
Timeline 2: Lavos Timeline. This is the default timeline of Chrono Trigger, the one that would occur without any modifications by the heroes of that game. In this timeline, Lavos lands in 65,000,000 BC, and burrows into the Earth. Later, in 1999 AD, Lavos awakens, and destroys the planet. Over the course of the next 400 years, the planet slowly dies, until sometime after 2400 AD when it is considered to be completely devoid of any life of any importance.
Timeline 3: Lavos Timeline Averted. (Keystone T-1) In this timeline, Lavos lands, but is destroyed by the heroes of Chrono Trigger. The nature of the Chrono Trigger game allows this to happen in many points, but in the official storyline (and in Chrono Cross) it is assumed that this happens in 1999 AD, as he bursts out of the planet's crust. Humanity is not destroyed by Lavos, instead they advance to hypertechnology levels. Around 2400, they build a great city/research laboratory named Chronopolis. During an experiment designed to control time, Chronopolis causes the Time Crash, which damages time and sends Chronopolis and Dinopolis back into time (at approximately 7600 BC). This causes may repercusions, which are the focal point of Chrono Cross.
Timeline 4: After the Time Crash. (Keystone T-2) In this timeline, the Time Crash happens in another dimension, which forces this dimension on a different path. The chaos created by the time crash and the two hyperadvanced cities of Dinopolis and Chronopolis landing in prehistoric times causes many, many disasters, including a rather large storm. This storm causes several problems with Chronopolis, which eventually leads to the Chronopolis supercomputer coming to need Serge. Depending on if Serge survives or dies, this dimension splits into two others, "Home" and "Another."
Timeline 5: Home. In this dimension, Serge survives. Chronopolis and FATE are not around because of this, and many of the characters in Chrono Cross: Home's world are different because of the lack of FATE's (behind the shadows) influence.
However, the damage due to the time crash causes tears between this dimension and Another, which Serge eventually begins to use.
Timeline 6. Another. In this diemsnion, Serge dies. This causes FATE to be locked out of several of it's key systems. FATE begins to look for a way to bypass this.
Timeline 7: Ideal timeline This represents the timeline that occurs after Chrono Cross. the differences between Another and Home are merged together to form this timeline. Presumably, Serge survives, and Chronopolis is eventually created (the Time Trash also reoccurs to prevent a paradox, but time continues after that as normal.)