There is no real reason for us to travel (or aliens to travel from) other galaxies though, since there are plenty of solar systems and planets that could possibly support life in our own galaxy. Travel between galaxies really only makes sense with worm holes, other ways to bend space/time, or possibly ways to phase out of the universe all together (allowing it to move/rotate etc without you for awhile) and then phase back in, possibly an extreme distance away (even though you actually didn't move at all...everything else has drastically).
In theory...everything is relative...and all movement in the galaxy is relative to the initial explosion/movement....meaning that everything may be moving at a specific speed and direction..which could possibly be incredibly fast. Lights limit on speed could only be relative to other objects that have created light...meaning that if you where able to phase out...you could possibly travel thousands of light years in a second. Of course you would have no control over your direction etc, but....it's possible you could determine the direction/rotation etc..and plan for it...to determine how far/where you would show up after being out for so much time.
Anyway....as someone else mentioned, there has been plenty of time for sentient life to develop elsewhere..since we as an intelligent species have been around for such a short time. It seems highly unlikely that a very easy method of traveling vast distances is possible....as if it was possible it makes sense that any race that discovered it (or races) would quickly spread all over the place. While space is vast.....the amount of time such a race would have to expand, and the exponential growth as more and more planets where used as expansion points, would lead to eventually the race spreading throughout the entire universe.
I think, because of this, that travel at speeds faster then light is not possible. Travel through worm holes etc...is also not possible (at least survivable for any form of life). It makes sense that we are limited to traveling at speeds slower then the speed of light...and therefore, we are limited to only our own solar system and those that are relatively close to ours.
In addition, it makes sense that life is very rare indeed on planets....and that sentient life....is even more rare. Even when you do have sentient life, it's probably rare for the planet the life exists on to have the resources needed to eventually develop science to the point of long distance space travel (or for the life to ever reach space at all).
In such a case you might have something like a 1 in 10 million chance for a solar system to have a planet that can sustain life, and then actually develop life. Then you have a better chance for life to eventually develop that can use tools and develop higher thinking/science (say 1 in 1000). Then you have a fairly good chance that the planet the life develops on has the required materials, resources to reach space (say 1 in 100), and finally a fairly good chance that such a race would survive long enough to actually do so (1 in 10). All that together means something like a 1 in 10 trillion chance of actually having a planet support sentient life, that develops technology and survives long enough to reach space.
Now since it's estimated there is approximately 100 billion stars in our milky way galaxy...there is a very good chance we are the only planet in this galaxy that supports sentient life (let alone sentient life that can use tools, developed technology to the point of reaching space and survived long enough to do so).
On a galactic scale we are still babies....the question is...will we actually survive long enough to colonize other planets/moons in our own solar system, let alone beyond. The odds of that are not very good in our favor right now (I certainly wouldn't bet on it). If we do...it's likely that we might eventually dominate the entire galaxy.
There are estimated to be well over 100 billion galaxies in the universe btw....so it's VERY likely that life has developed in other galaxies...and in some of them reached the stars....terraformed other planets and started to spread throughout their galaxy. It's quite likely that there is at least one galactic civilization out there...and even probably one galaxy where more then one form of sentient life started to expand and met each other in space.
The chance of that happening here...in our galaxy is VERY small though (go buy a lottery ticket and your far more likely to win then you are to have that happening). So it's not very likely at all that aliens have visited earth...or ever will. I'd say we still are talking about less then a 1 in a million chance that we will ever reach another solar system let alone colonize one ourselves.