Only zero-mass particles such as photons can reach the speed of light, and for them no time passes between events, that is correct. Zero-mass particles must necessarily travel at the speed of light, neither less nor more, so for them FTL is not a relevant question. For anything with mass to exceed the speed of light would require first reaching that speed, and to do so would require infinite speed. Infinite speed in turn would require infinite energy, which is unavailable, because our observable universe is very finite indeed. It is less than 20 billion light years in radius and its density is very low on average. If we could exceed c, we would be in a sort of looking-glass world for which there is no persuasive evidence so far. Even apart from the question of how to get there, it is hard to make much sense of the implications if there were such a world. There the ideas of speed and time would be thoroughly alien, with speed increasing as one loses kinetic energy, so that your speed increases to infinity as you "slow down" to zero energy (momentum).

Make of that what you will!

Slowly!!  

Jon  

It's that man again!! [Irritation hinted at for comic effect only. I am only irked by those who fail to use their minds, or who use them to the disadvantage of others.]

Some early versions of String Theory demanded (by symmetry) the existence of tachyons, which were the anti-particles of "normal" particles. One characteristic of a tachyon is that it moves at c.squared/v, where v is the velocity of their counterpart. So their speed range had to be between c and infinity. No evidence they exist, apart from some conjectured equations.

Remember that the time dilation effect is only true for the photon (or hypothetical object) moving at c. The rest of the universe (including the places the photon will visit) age normally while it is in transit. If you could fire me at some far-distant star at speed c, I will still be 61 when I get there, but it might by then be a red dwarf.

Also, if we are to believe New Scientist: you would be dead almost instantly, so it probably doesn't really matter

http://www.newscientist.com/article/dn18532-starship-pilots-speed-kills-especially-warp-speed.html