Escape from the Planet of the Apes - I personally feel like this is the only sequel to The Planet of the Apes that came anywhere close to the level of the original. I love Beneath the Planet of the Apes, but only because it is pure camp and I find it amusing.
The Voyage of the Dawn Treader (being the third book in The Chronicles of Narnia) - (Never seen the film for the record, am only talking about the book) after a fairly dry followup to The Lion the Witch and the Wardrobe with Prince Caspian, The Voyage of the Dawn Treader was an extremely thrilling ride for a very small version of me the first time I read it. Still my favorite of the series.
Fallout 3 - While a lot of old time Fallout fans moan about what a horrible continuation of the series this game was, but I have never been able to help but absolutely love it. One of the most enjoyable gaming experiences I have ever had. I tried playing the originals a bit, but they just aren't the type of game that I have ever had any interest in, so it stands to reason fans of those games aren't fans of the one I enjoy.
Monkey Island III: The Curse of Monkey Island - A lot of MI fans, myself included, have never considered this on par with the first two, but personally I still found it extremely enjoyable to play. I consider it The Return of the Jedi of the Monkey Islands.
Rogue Squadron III was pretty impressive.
Dark Forces III: Jedi Knight II: Jedi Outcast was also pretty amazing, but unfair to list since it was the first, second, and third parts of three different series, so it probably shouldn't count.
The PlayStation 3 was a bit of a let down as a followup for the phenomenal PlayStation 2.