Could there be a collision of planets?
No, there is no reason for such a fear. The planets and stars are so far away from each other, even though we don’t realize it.
Planetary collisions are pretty rare, especially in developed systems like ours. Our solar system is reasonably stable -- not perfectly so, but all of the planets are not likely to hit another large object in the near future. About the worst thing that could happen would be that an asteroid could hit. Since an asteroid or comet impact can produce global level effects, but even a mass extinction would be nothing compared to what Mercury could do to us. But, since most asteroids that are likely to hit a planet are all far too tiny to be called a planet in any sense of the word, we wouldn't count those.
Generally, this seems to be the norm in developed systems. Of the extrasolar planet systems we know about, they don't seem full of planets that are prone to collisions. In fact, you see all kind of complicated motions that keep planets from colliding with one another.
image source: wikimedia commons
Any collisions between planets happened early in the Solar System, and they most certainly did. Our Moon was made by something Mars-sized smacking into the Earth very early on (over 4 billion years ago), and Mars has a giant, very old (about the same age, but ages are pretty uncertain once we get away from the Earth and Moon) crater that makes the northern part of the planet quite a bit lower than the southern part. So, when the inner solar system was forming, all four of the inner planets were probably getting hit a lot by comparable-sized objects (and smaller stuff as well). Thankfully, most of that stuff either collided with something or was eventually knocked out of the area by Jupiter, so it won't collide with a planet any more.