2nding Assassin’s Creed 2 being better than the first game.
Thor 2 was much better than Thor.
Nothing that hasn’t been said but…
Mass Effect 2 was a masterpiece in gaming and is the best of the series
Spider-man 2 is arguably the best superhero movie ever made, and is the best of the series
I feel like Lethal Weapon 2 was the best of the series, and by a wide margin.
I personally think that Shrek 2 is significantly better than the first.
Many think that Bride of Frankenstein was better than Frankenstein.
Only if you mention the Richard Donner cut. It works much better with Marlon Brando restored to the film and with Richard Lester’s comic bits removed.
Batman: Arkham City is, so far, the best of the series regardless of whether you count the quasi-prequel Arkham Origins.
While Dune is arguably the best of Frank Herbert’s Dune Books, the Sci-Fi Channel’s Children of Dune miniseries was superiour to their Dune miniseries.
Personally, I like Bill and Ted’s Bogus Journey more than Bill and Ted’s Excellent Adventure. Though technically, those don’t count because of the OP’s requirement of more than two entries. 
Ninja Gaiden II was the highwater mark of the Ninja Gaiden NES games (recently rereleased as a download for the 3DS).
Bases Loaded II was the best of the Bases Loaded series. Also NES.
I’m old.
Your loss. 
STREET FIGHTER II is beyond iconic.
Rocky 2 edges out Rocky 1 for mine
Clerks 2 edges out Clerks. Not wild about any other Kevin Smith movies, but these two are great.
While From Russia With Love is superior to Dr. No, the series didn’t really hit its groove until Goldfinger and (Sean Connery partisans can quit reading now) it didn’t peak until the first and third Daniel Craig installments. Berniece Marlohe is easily the best-looking Bond girl to date, and Eva Green is the most riveting. Even the interim installment, A Quantum of Solace, was pretty damned good.
It’s a bit old and cuts off after Part Two (spoiler: the main character dies), but the Quijote is generally held as an exception to the rule that “there was never a good Part Two”.
Clerks 2 doesn’t count since there is not yet a Clerks 3.