Some cometary apocalyptic scenarios:
Halley's comet made a relatively close approach in 1910 and the Earth passed through its tail. A slight bump to it's orbit and it would have been very bad news. It came even closer in 837 at 5 million km. If the core (or even a fragment) had hit the Earth, it would have caused extensive extinctions, year or decade long winters and just a generally not fun time.
Comet Hyakutake in 1996 came within 15 million km. Doesn't seem that close, but it was only discovered 3 months before its closest approach. With a core 4.8km in diameter, it would have been very bad news if it had impacted.