This article is accurate for the latest versions of EU3, Napoleon’s Ambition, In Nomine, Heir to the Throne and Divine Wind.
The timeline in Europa Universalis III has been changed several times. In the original version the time-span was from 1453 to 1789, and Napoleon's Ambition extended this to 1821. The second expansion, In Nomine added roughly 53 years at the start, expanding the timeline once more, now from 1399 to 1821.
Heir to the Throne and Divine Wind do not modify the game's time frame.
How To Extend The Timeline
To extend the timeline beyond 1821, open the file common\defines.txt in your EU3 folder. Change the 2nd line from:
end_date = 1821.31.12
to the end date of your liking.
However, if you manage to play long enough, the technologies will run out and the game will crash. To stop this, you have to add new technology levels. For all the files in the common\technologies folder, copy and paste the last lines, adding new tech levels and increasing the expected year by at least 20.