Not actually impact itself, but near so. Imagine an asteroid (or meteor, or whichever is the correct term) large enough to cause worldwide extinction if it hit were heading towards Earth. At a point where it would be visible to the naked eye, what adverse effects would that have on us and the Earth? Would it be near that point or considerably before/after that that there would be significant bad effects?
None. These objects are just too small to have any impact (pun not intended) on us, until they hit us. It’s their inherent kinetic energy that makes them dangerous. Now, pieces of it might break off due to tidal forces and enter our atmosphere, but this is going to be little more than a light show.
Well, a 10-meter-diameter asteroid came within 88,000 KM of Earth in 2003, and a 30-meter-diameter one within 40,000 KM in 2004, neither being visible to the naked eye nor having any noticeable effects on the planet.
There are much larger ones in near-Earth orbits (i.e., orbits that from time to time bring them near Earth) but only once in astronomical history have any of them approached closer than the Moon’s orbit.
2002 NY40, an 800 meter wide rock, showed up in binoculars and small telescopes at 10th magnitude when it passed within 530,000 kilometers of earth (1.3 X moon distance).
One coming close enough (and by this, I mean into low Earth orbit, so significantly less than one Earth radii) might fragment from tidal stresses and shower Low Earth Orbit with debris that could knock down satellites and possibly pose a navigation hazard to spacecraft, but this seems unlikely; even if it did break up, the individual components would have enough kinetic energy to swing by and shoot off into interplanetary space rather than remain in orbit.
Something large enough to seriously affect Earth by gravitationaly interaction would be huge; the size of the Moon or larger, and would have to come very close. There are no known “loose” bodies of that size in the Solar System, so it would also be flying past at interstellar speeds, which make it both unlikely that it would intercept the Earth and that (assuming it doesn’t strike) it wouldn’t hang around long enough to do much interacting.
Stranger
Without a doubt the end result would be a post-apocalyptic wasteland divided into kingdoms or territories–the majority of which are ruled by wizards. But don’t worry: one man bursts his bonds to fight for justice! With his companions Ookla the Mok and Princess Ariel, he pits his strength, his courage, and his fabulous Sunsword against the forces of evil. He is Thundarr, the Barbarian!
Since you identify yourself as living in London perhaps you’ve never seen Thundarr. The the show was set years after a catacylsmic event caused by a “runaway planet”, not an asteroid, passing near Earth, breaking up the Moon and destroying modern civilization. The disaster was depicted in the opening credits of the show. As a little kid, seeing the Earth’s near destruction was very scary (all too real for a kid who was very scared of nuclear war and the possible end of the world). I didn’t much care for the cartoon at all as a result.
Luckily we don’t need to worry much about “runaway planets”…the threat of actual asteroids actually hitting Earth is a very real worry though as other posters have said.
Well, aside from a whole bunch of pairs of stained undies.
Geeze, how close are we talking for a KT-sized asteroid (7-10 miles across) to be naked-eye visible? 
How ‘near so’? The Tunguska event may have been a comet nucleus exploding before it hit the ground. A large asteroid plunging across Earth’s atmosphere (q.v. the film 2010) is sure to generate massive shockwaves and much heat.
A sufficiently massive object passing sufficiently close will affect the Earth’s orbit, but I’ll defer to Angua for the details.
A meteorite that “plunges through the atmosphere” can pretty much be considered as impacting (or at least, intersecting) the Earth; the likelyhood that it’ll skim back off into space (especially if it has hit atmosphere thick enough to create a shock wave that can destroy objects on the surface) is essentially nil.
See Post #5. There’s nothing in system that is on a potentially Earth-intersecting trajectory which is large enough to have a significant influence on Earth. Even something the size of the Moon would have to pass by the Earth well within its sphere of influence to have any effect at all
Let’s work an example: (I’m going to make some gross simplifications here, specifically that the initial trajectory is locally flat, that Earth’s influence on the trajectory is minimal, not accounting for the relative movement of Earth or its vector addition or subtraction on the passing meteor, et ceetera, but this should be a close order of magnitude estimate.)
If an object the size of the Moon, for instance, made a “grazing approach” (within 1000 km) of the Earth at the Solar escape veloicty (42.1 km/s at Earth’s orbit), it would be at a range such as its gravity had a significant influence on the Earth for about 52 minutes, with a maximum imposed acceleration of about 1.7% of Earth gravity at perigee, increasing and declining symetrically as a cosine function over the period of influence. This isn’t insignficant, of course–you might actually feel the slight negation of Earth’s gravity as it passes overhead, like a gentle elevator ride–and it’ll certainly have some geophysical effects as well as disrupting the carefully planned orbits of satellites, but in no way is this going to affect the Earth’s orbit about the Sun in a way measureable by anything but the most sensitive instruments, nor is it likely to have any measureable effect on the Moon unless it happens to engage that sphere of influence.
The same object making a pass at 10,000km will have a maximal effect of about 0.4% of Earth gravity with roughly the same duration. At 50,000km, the duration is about 34 minutes and the maximum applied acceleration is 0.02% Earth gravity. So, even an object the size of the Moon is going to have very little influence on Earth. A grazing approach by something truely massive–a free-ranging superJovian planet or a passing brown dwarf–might seriously grab the Earth and send it spinning off in some catastrophic, wildly elliptic orbit, but the odds of that happening are, well, astronomical.
Stranger
From Wikipedia article on Apophis:
It’s going to have another close approach in 2036, but I couldn’t find out how close it’ll be on that pass. It’s orbit will be changed by the first flyby, but the experts are pretty certain it won’t hit on the second pass.
Its size is around 320 meters, which is smaller than the Chicxulub dinosaur killer, but still large enough to do lots of damage if it ever does hit. But it’s not going to do any damage unless it just happens to hit a geostationary satellite on its way by.