Well presently we are still waiting for the Voyager satellites to leave our Solar system, as yet has anything that we have created (other than noise) drifted outside of our solar system.
You ask if intergalactic space travel is possible, but that would be like running before we've learnt to crawl. Once we know how to move from Solar system to solar system then Galactic travel would be a next step. (although this might not be seen for centuries)
Remember a Galaxy is many stars, that are many solar systems, so to travel from one Galaxy to another you'd have to travel past many different solar systems to arrive there. (which would take many hundreds of years even at our highest speeds)
Of course many people are looking at the theory for Wormholes and teleportation of matter, but the problem here is that for either of these you would need some form of Gate or door, which means that it has to be delivered first.