TeknoNurd
Thousands of years from one star to the next, TeknoNurd? A few tens of years, actually, if the ship travels close to the speed of light - which is definitely possible. The Milky way is 100.000 light years in diameter - that means a ship could traverse the entire galaxy in ~100.000 years outside time (significantly less ship time due to relativity).
An advanced civilization could send numerous ships to explore/colonize the galaxy. Each of these ships will explore a swath of the galaxy until they reach their destination. And once in the target system, the crew of the ship could start a colony, that will build/send ships further out in only a few hundred years. And the cycle repeats itself.
Now - let's say the homeworld sends 10 ships (per average) every year. In 100.000 years, this civilizaton has sent 1.000.000 ships to explore the galaxy. You can add to that number the ships the colonies will build - and you'll see that in a few million years, an interstellar flight capable species has not only explored the entire galaxy, but has established a presence everywhere in it.
And that's just one species. What if there are thousands on species capable of that? If intelligent life is abundant, the chances of making contact are significant - with or without FTL drive.
When one talks about sufficiently large amounts of time, the feasability of FTL is irrelevant.
And our galaxy is old - life (even intelligent life) could have appeared 5-6 BILLION years ago (all the required conditions - that we know about - were met).
First, Resources... you don't have enough. 10 generational ships a year? Do you have any concept the impact such an effort would have on an economy? Imagine taking a few trillion $ of the world economy for a number of years, then shooting it down the crapper. That's what an expedition to the stars is because the home planet receives zero benefit. There is no way an economy could muster 10 generational (or colonization) ships of a year. If they could manage one ship in 10 years, it would be a bankrupting acheivement... Even going that fast would likely be a last ditch effort if their world is ending for some reason.
Second, Speed... you can't go that fast. We're talking a big, big ship to hold enough population and resources for colonization. Just under light speed is a small ship making a dash. A big ship with human life aboard, you cold only accellerate so fast, then decelerate so fast, in fact most of the trip would be doing one or the other, and it would take a lot of time.
Third, Time... you don't have enough. Just our technology has advanced exponentially (and will continue to do so), there are a number of ways we (and any other civilization) have and will have to end us. Even without completely ending us on purpose or by accident, how long do you think we can support 10s of billions of people on this planet and still put any effort to a colonization ship? These would be issues not unique to us.
Fourth, Time... We may not have enough. While the universe may have gobs of space and time, species may not. Look how many times our planet was knocked to it's knees. Such things may be more common place that it appears to us, heck that could be the missing element of Drake's equation. Maybe, intellegences don't have time to develop as often as we think, or time to become self-sufficient space farers. Look how long it took for us to appear after the last Earth strike. Will we have time to get self-sufficiently off the planet? Is doing so even on our radar?
Fifth, motivation... We don't have enough. Right now, we are still focussed on survival. Does an intellegent species, aware of their mortality, ever start thinking of species survival rather than self survival? Really, would the USA (or its voters) allow the choice to have the citizens live as a third world economy to fund even one generational/colonization ship? And, when we do that, can we count on adversarial countries to let us? Would this be an issue for aliens? Most likely, since evolution counts on competition and survival of the fittest, it's likely most alien civilizations would not be utopias of peace, just like us.
Sixth, the mission... Exploration doesn't justify a generational ship. You bankrupt your world to create the generation ship, and they go exploring. Thats a lot of accellerating and decellerating. It will take years for your finding to get back to earth (if that is possible at all). If you've got a self-sufficient generational ship, you don't need to explore, you just need to find a planet that seems likely to setup home at. And, since your ship is self-sufficent, finding a new planet is not all that criticial anymore. So really, you're ship can explore forever.
Seventh, the mission... Colonizing is not that quick a process. You're talking a small population taming a world. It's gonna take a lot of time to get the society where the need to create another ship (or relaunch the original). You've travelled thousands of years, your ancesters have checked a few star systems, but nothing homy. You finally found a homy place, and have settled it. Until resources get low, or something goes terribly wrong, are folks really gonna want to get on the ship again? I'd guess that any colony would be a few thousand years old before it would be time to send the ship off again. I wouldn't let the ship go before because, well, it's a great life raft if something goes wrong.
Eighth, oops. You're travelling light years in a pretty fragile bubble of air. Is simply surviving the trip realistic?
Space is a big, old place. It is loaded with room and time. With all that room and time, I think it's likely intellegent life springs up all over the place. Without FTL travel, everyone is pretty isolated.
Now, in 40 years we'll be able to upload our minds into computers. Computers are much less fragile in space, and time is much less of an issue to a computer. Even though flesh and blood humans won't get out there, computers with our intellect will. By then, we may have common access to that intellect, and may be able to see, hear, smell, taste, and feel other planets... or at least recordings/transmissions. But, alas, even this is not something ETs seem to be doing much of as we've not had a bunch of their "probes" dropping in. This may be an argument against there being other space faring species out there.
If "a sufficiently advanced" society could do whatever, then it would be getting done thousands or millions of times over or thousands or millions of years. So whatever their doing, it's not getting them to our neck of the universe.