Personally, I think that, if it's possible to go faster than the speed of light, such technology is so extremely rare and hard to accomplish (requiring LOTS of energy, at the least), it's practically non-existent. This would solve Fermi's Paradox very quickly.
Of course, there are ways to supplant such ideas, but they're very very hard. Unless you rely on robotics to seed other worlds, you'd need to be put into a deep sleep to save on resources as you stay on a ship for, at the VERY least, years on end. (Think about it; to go the speed of light, alone, you'd be talking about 4 years to the nearest planet, and the speed of light is theoretically impossible to accomplish).
I'm not sure what the maximum delta-v we can accomplish is; I'm sure we will develop more and more efficient engines (even if they only emit a little bit of thrust, as an ion engine does), but we have a long ways to go to achieve a sufficient delta-v to really go anywhere.
Of course, one can seed a world through information. For instance, send out a ship with our DNA stored, and some basic materials, and have them "build" life on a new world. But then, terraforming would be required, and if you were to launch yourself into a world where life already exists, you're more likely to die than live there (it would be like the Native Americans meeting the Europeans, only with no immune system for ALL the germs, even assuming that they weren't incompatible in other ways, such as one being ammonia-based life form...)
Furthermore, this is assuming ability to space travel in the first place, which may not be possible form lack of resources. And yet, even furthermore, perhaps a species doesn't WANT to leave. On Earth, we have debates that we should "fix the world" before we bother with space... seeming to say that we need to eliminate disease, poverty, hunger, etc., which are very unlikely to be solved anytime soon. And even then, an alien race might just desire to download itself into a very large synthetic computer, and live in simulation. (Or, as in Greg Egan's Diaspora, they may try to colonize as digital beings, which seems to be the greatest hope anyone has... but even then, spreading would be very difficult, as you would need to set up the satellites to receive the data, translate it, and "construct" you, and even then there's the chance the download might "corrupt" you).
Or, perhaps their world didn't survive their equivalent of our Cold War. Maybe some alien civilizations destroyed themselves, through warfare or pollution.
The "They should overtake the universe!" people really are extreme optimists. Space is a cold, harsh mistress.