Cloud or his weapons make numerous cameos in FFT (as a playable character), FFVIII (Ultima Weapon's sword), and FFIX (the weapon shop sword).

I doubt that this was part of a deliberate attempt to integrate these worlds. Even in FFT, the device that brings Cloud over moves objects through space, not time.

There's a weak attempt to connect the storyline of FFX-2 with FFVII with a single character name and a brief conversation, but it's dubious at best.

The Ivalice games create a series of connected storylines set in a single world. Although the Suikoden series is the best non-FF example of this.