What would happen?

Besides the view in the sky changing, not very much. It would take a very long time for our solar system to actually leave the galaxy, if it was headed in that direction. Otherwise the fate of our solar system would be largely the same as if it stayed in the galaxy. The planets would still be gravitationally bound to the Sun. The Sun would continue to burn through its fuel like normal and would remain active for another 5 billion years or so.

IF that happened, the sun and its planets would be floating between galaxies. Nothing would happen to the Earth of course, it would still be gravitationally connected to the sun.

We'd be floating through the intergalactic void, yes, but as long as we at the very least had the Sun going along with us and we maintained the same orbit around it, life would go on pretty much the same for life on this planet. The night sky would be changing, pretty much as slowly as it does now, but other than that not much else.

Not going to happen anytime soon.

Well... we really wouldn't "drift away" - we're in orbit about the center of the galaxy. If something extraordinary occurs - a close encounter with a more massive star, perhaps a black hole - our solar system would likely be disrupted quite a bit - we may not lose any of planets, but they may be scrambled to new orbits in the process; but, I would think the inner planets would follow the sun in such an event.

This may happen in the collision (2 billion years from now) between the Milky Way with the Andromeda galaxy. Having the solar system cast into intergalactic space would not affect conditions within the solar system very much, but would make interstellar travel much more difficult than it already is.

yep.....

but dont worry about it, you will be long dead by then

the sun will have swallowed up the earth, and turned it into a smouldering cinder, as it becomes a red giant.

but, yes, hypothetically it could happen

Hypothetically... it would be OK. As long as we keep our sun, and our orbit didn't change around it.

All that would happen is that we'd see different constellations and asterisms.