The opposite of the season opener, traditionally a Big Two-Parter or even Three-Parter in its own right as well as possibly the end of a series arc, this could be a jumping-off point for players or their characters, and will certainly be a major conflict with possibly life-changing ramifications. It's possible for the core cast of travellers to survive unscathed and go on to more adventures, but endings tend to be where things end...
Whatever's happening, up your budget. Blow up as much as possible. Set the TARDIS on fire. Add more whooshing spaceships to an intergalactic chase scene. Why have one gigantic army of monsters when you can have two, two when you can have five? Give the viewers the Shadow Proclamation as Russell T Davies wanted to, not as he could afford to!
The Series Finale may or may not have a series arc to pay off. If it does, it should ideally be a big deal, like Harold Saxon's election, rather than a bit of a minor point like all the references to Torchwood who we could have found out about cold.
It also lets you bring back popular monsters and villains for another shot at the title. They might have appeared earlier in the run, or they might be special guest stars. But equally, the threat could come from something new.
Whoever or whatever is involved, the threat is generally a big deal. It may be difficult to top The End Of Time for a villainous plan (the destruction of absolutely everything ever including the perpetrators) so feel free to go big but not that big. High stakes, big weighty decisions...
The personal stakes should be big too. Go for broke here - love, death, regeneration, having to leave the TARDIS, characters reassessing their entire lives. Encourage everybody to let out their characters' bottled-up feelings, bring back NPCs they love, or love to hate for final meetings, present opportunities for suicidally crazy heroics in the final battle...
If this is the end of the game, lay it on extra thick. If it's just the end of the current run and you have definite plans to come back, just lay it on thick in general, and save extra-thick for anyone who won't be able to play in the next series.
(This can also apply in a non-finale episode that happens to be a player's last time at the table. If someone's moving away, this is a good time to set up a universe-threatening time storm for their character to volunteer to throw himself into and seal the rift with his bare hands.)
A massive change in the status quo could also be a good thing, but a happy ending should feel earned. And a devastatingly sad ending should be followed by a trailer for the Christmas special.
Example: The Final Hour
The Mysterious Man realises almost too late that the actions of the Daleks, the clues in the ? Files, the warnings in The House That Screams and the threat of the returning Dark Rider all point to time itself being unravelled, and travels back to the birth of the human race to try and stop it.
Finding the Dark Rider at the head of a cavalry charge into the valley where the first humans are about to be born, fighting an advance force of Daleks (lead by a Dalek Overlord with a cool new armour design) seeking to prevent the human race existing, the travellers have to stop them both, then prevent the sun being turned into a black hole, setting off a chain reaction that will destroy all life in the galaxy. Will the Mysterious Man sacrifice himself to stop the process and save the universe? Will Emily tell Rajiv how she feels? Will Mafek get his revenge on the Seneschal for the death of his planet, or die trying? Will anyone survive?!