In the early 23rd century Pluto will switch ranking with Neptune and temporarily, for about 20 years, will become the 8th planet from the sun. The last time this occurred was during 1979-1999.
Based upon current orbital calculations which gives it a year equivalent to 286 Earth years, in 2288 , the planetoid 50000 Quaoar will have completed one complete orbit of the sun since its discovery in 2002. Similarly, the year 2252 will mark a full orbital cycle since the 2004 discovery of the planetoid 90482 Orcus, which as of 2004 had a calculated orbit of just under 248 Earth years.
2221: Triple conjunction between Mars and Saturn
December 2nd, 2223 At 12:32 UTC Mars will occult Jupiter
2238/39: Triple conjunction between Jupiter and Saturn (last triple conjunction between Jupiter and Saturn was in 1981)
August 12th, 2243 - At 04:52 UTC Venus will occult Saturn
If the Jewish account of Creation is true and the world was created in 3761 BC, it will have been 6,000 years since then in 2239. Some people believe this is when the world will end.
The Fifth Element (2263, the beginning is set in 1914, then shifts to "300 years later", however an alarm clock in the film shows the year as being 2263, rather than 2214)
Red Dwarf (before the accident) in which Lister states that he is "an enlightened 23rd century man" (yet earlier episodes said 21st century). Though for the most part, it is set 3 million years later.