Majora's Mask is the greatest sequel ever created.

Listing my top five favorite sequels would be the same as listing some of my favorite games of all time, so instead, I'll list some games that are far better than their original release.

Arc the Lad 2. Arc the Lad is a TRPG series, and like most TRPGs you can choose where you want to go next, but normally it's limited. The first Arc the Lad had where you could choose which continent you were going to and then each dungeon or location from there. There was limited movement similar to your standard JRPG in a couple of screens. The second in the series is a major overhaul from the first game and TRPGs in general.

Arc the Lad 2 has all of the same continents and others, but it's filled with towns, dungeons, etc. The continents themselves are world maps, and like your standard JRPG rather than your TRPG, towns and dungeons are fully explorable. Arc the Lad 2 has a hunters guild, multiple dungeons that aren't required to complete the game, a monster taming/monster class system, etc. Because of the games popularity and the monster taming system, they developed a sequel that used your Arc the Lad 2 data called Monster Tournament, or Arc Arena in the US, you had to purchase Arc the Lad Collection so you got it along with it, while Japan it was seperate. Arc Arena allows for you to load your save data and go through preset rounds against opponents which get tougher the further you get, getting special items and upgraded monsters which are usable in the main game, an endless battle mode, with the reward being more powered up treasures, and then a versus mode where you can load two(or even the same) save data to player one and player two, allowing you and a friend to pit your team against one another to see who has the better characters.

Lufia 2, Infamous 2, Final Fantasy Legend 2(SaGa 2,) Uncharted 2, Twisted Metal 2, Diablo 2, and Warcraft 2.

Since there are so many, I'm just going to focus on direct sequels that improve on their predecessors.

Street Fighter II
Half-Life 2
TimeSplitters 2
Super Smash Bros. Melee
Ratchet & Clank: Going Commando

Thinking it over one thing about games that is distinct from film is while in film sequels often struggle to capture the original's quality, in gaming in almost every series I enjoy the first entry is not my favorite.

I prefer Super Mario Bros. 3 over Super Mario Bros.
I prefer Link to the Past over original Legend of Zelda
Super Metroid over Metroid
Mega Man X over Mega Man

I am trying to think which series the original is the best entry?

Quite a few!

Civilization IV: The culmination and apex for the series for me; it took the existing concepts from Civ III and improved almost every single one of them, it had awesome visuals and great music and the gameplay was super addictive. It also housed on of the best user made mods of all time for any game: Fall From Heaven II, if you love Civ and still haven't played this gem, do it now (Arnold voice)!

Half-Life 2: With the revolutionary Half-Life setting the standard since 1998, everyone, me included, wondered if Valve could pull another rabbit out of the hat. They could. Incredible gameplay with levels of interactivity that other games could only dream about, fantastic and underrated soundtrack, brilliant story and storytelling and revolutionary implementation of physics. For me, Half-Life 2 is also the golden standard for pacing, especially Episode 2 stands out here.

Timesplitters 2: The best console shooter in ages and the new Goldeneye of local multiplayer. Brilliant maps, awesome and varied game modes, cool character and stat system, multitude of weapons and brilliant visual design form one of the few terrific console FPS' I ever played.

Diablo II: Still the best hack & slash game ever made, this is the one game I've spent the most time with in my entire life.

Uncharted 2: Improving all the pieces that made Uncharted thoroughly enjoyable, Uncharted 2 quite simply set the standard for 3rd person shooter/adventure games and made me appreciate a genre I was never very fond of.

Resident Evil 2: The best in the series for me, amazing gameplay, fluid and challenging (unlike the first one), great music score, cool story, awesome characters and incredible atmosphere.

Silent Hill 2: The defining "holy shit" game of the horror genre, I have never been so creeped out by a game's atmosphere before (until Amnesia came along). Fantastic music, great acting and writing and awesome visuals. It also made some fairly revolutionary use of SFX to set the mood.

Baldur's Gate 2: Sequel to the best RPG in the world at the time, it inherited the throne with grace and dignity. Massive scope, amazing writing, epic gameplay, awesome atmosphere and some of the most memorable characters in any game ever made.

Thief 2: Added a lot to the original, unique setting combining tech and magic, awesome writing and the best stealth gameplay in any game to this day and sprinkled with a downright unbeatable protagonist.

TES: Daggerfall: Ambitious and quite simply mindblowing in size. Despite its problems, it remains one of the most amazing RPG experiences I've ever had.

Vampire the Masquerade: Bloodlines: "Sequel" to the more obscure isometric view first VTM game and a solid RPG. Fantastic characters and acting, great gameplay and cool setting. The only game with truly badass vampires and werewolves.

Gothic II: Easily among my top ten RPG's of all time, large world, simple and enjoyable gameplay, good story and cool characters.

GTA: Vice City: Where the series really started coming together, they added motorcycles and fine-tuned the technical aspects of 3D open world gameplay, improved shooting mechanics, fantastic soundtrack, varied missions, enormous time value and super groovy main character.

Heroes of Might & Magic II: They added unit upgrades, expanded the roster of races, added a slew of events, buildings and spells and heroes. Tactical awesomeness sprinkled with good music and the best hot-seat multiplayer of the time.

Neverwinter Nights 2: RPG gaming at its best, this is how it's done. Cool characters with their own sidequests, deep and engaging gameplay with a bigger focus on tactics than the first one and a rich world with some unique features (building and maintaining your own keep was really cool).

Team Fortress 2: Quite simply the most entertaining online FPS experience around. Silly and quirky visuals, great humor, balanced gameplay and awesome maps.

Deus Ex: Human Revolution: One of very few successful "back to the roots" attempts of the gaming industry, this title resurrected and preserved the feel of the original while pouring in modern aspects of gameplay. Incredible writing, even more incredible music and inspired visual design. Perhaps the biggest pleasant surprise in the entire 7th gen for me.

The Witcher 2: Assassin of Kings: This is a game that every RPG lover in the world ought to play, it has unique gameplay and combat, incredible writing, fantastic visual design and quality, great music and believeable characters. To top it off; the story is fantastic as well. This is head & shoulders above the likes of Skyrim and Fallout: New Vegas. Go play it now!

Gran Turismo 2: No other racer has even made me so ecstatic, the insane amount of cars and customization was simply unheard of at the time, even on PC, amazing graphics, great sound and a more fluid and friendly user interface than the first one. As a single release and for its time; this is very likely the best racing game ever published.

There are certainly more but these are off the top of my head!