Before providing a more detailed answer to your question, let me emphasize an important point: velocity is relative. Right now, you and I are both traveling at a velocity that is very close to the speed of light compared to the distant matter that is responsible for the cosmic microwave background we see. Or compared to the most distant galaxies visible.
So I will consider your question by looking at the velocities of objects relative to stuff that dominates the neighborhood. E.g., in the Solar System, velocities relative to the Sun.
Among man-made vehicles, the fastest spacecraft in an escape trajectory is Voyager 1. Its velocity relative to the Sun is just over 17 km/s. or about 0.0057% of the speed of light.
Its velocity relative to the Earth varies, however, since the Earth itself is orbiting the Sun at roughly 30 km/s, or 0.01% the speed of light.
And if we are really interested in Sun-relative velocities, the orbital velocity of Mercury is almost 50 km/s. So the Messenger spacecraft, in orbit around Mercury, is actually moving a lot faster than Voyager 1 relative to the Sun: at a pace of roughly 0.016% of the speed of light.
But never mind that. The Solar System as a whole (including the Sun, the Earth, you and me) is moving relative to the cosmic background radiation at nearly 400 km/s, which is more than 0.1% the speed of light.
Now there are some stars that move a lot faster. So-called hypervelocity stars may have been ejected by supernova explosions or other violent events, and some reach velocities relative to nearby matter that exceed 1,000 km/s, or about 0.3% the speed of light. Similar or even higher velocities are possible for very tightly bound binary star systems (e.g., neutron star binaries.)
Beyond that, if you look at the relative velocities of really distant objects, there really is no limit. As I mentioned above, the ionized gas that we see in the form of its cosmic microwave afterglow is receding from us so fast, its light is redshifted by a factor of about 1,100... this corresponds to roughly 99.9998% of the speed of light. But in this case, we are discussing the relative velocities of things that are many billions of parsecs from each other.
Thank u very much Sir. Please tell what happens to the 'Time Dilation' in the case mentioned in the last paragraph? What I could infer is that no two bodies can have a relative velocity equal to the speed of light.
Also, please tell if there is a chance that we have not noticed a heavenly body yet that has been moving at a speed near to light, that may strike the Milky way?
Time dilation, in this case, is responsible for that redshift by a factor of about 1,100 (from visible light all the way down to microwave radio frequencies) of the cosmic background radiation.
In our expanding universe, two very distant bodies may in fact travel faster than the speed of light relative to each other as a consequence of cosmic expansion. However, such bodies are mutually invisible to each other, as each is situated beyond the cosmic "horizon" as seen from the other body.
I am not aware of anyone ever detecting macroscopic objects faster than those hypervelocity stars that I mentioned. But even if one was detected... keep in mind that the Milky Way is mostly empty space. And it is incredibly big, a hundred thousand light years or so in diameter, many thousands of light years thick. So suppose we discover some monster star flying towards the Milky Way at a substantial fraction of the speed of light. The actual process of it flying through the Milky Way will take tens or hundreds of thousands of years, and with an overwhelming probability, the object will not run into anything, indeed it won't even get close to any of the Milky Way's stars. (This is also the case when large galaxies collide and merge... despite both having hundreds of billions of stars, the chances of an actual collision remain minuscule.)