As ARandomGamer correctly guessed on the second place is Etrian Odyssey Untold: The Millenium Girl.

I really love the Etrian Odyssey series. So in a way this game stands for all of them. This game is a remake of the first game with the modern engine of EO4. It also slightly enhanced the gameplay with newer elements. Additionally you have a new mode with a cut-scene driven story and pre-generated party. But you can play classical too.

The basic Etrian Odyssey gameplay is a great dungeon delver. You create multiple characters from different classes and choose five of them iinto your party (every time you go back to town you can switch active characters). You explore the labyrinth while drawing maps on the bottom screen of the DS/3DS. You have to fight regularly in turn-based RPG-fights. You gain experience and level up your party. You have to fight bosses to get deeper into the labyrinth.

The map-drawing with the touch-screen is an integral part of gameplay, you even get an early quest to draw a map.

The games all, so this one too, have the great level-design Atlus-RPGs usually have. As you explore the labyrinth, you encounter puzzles to move on and unlock shortcuts so that you don't have to move through known parts again and again.

As an improvement on the original game your skills are now presented in a tree, although the dependencies were already existant in the first game, but not graphically represented.

In the original and classic mode on certain events while exploring a dialogue with anime-faces would pop-up.

In the remake they added the story-mode which has real cut-scenes and additional story though.

This is an great example how a remake can enrich and add to the content of the original game while retaining it main identity and strengths.

The game itself manages to keep me invested through the gameplay, the great colorful monsters and environments. I really love the hell out of Etrian Odyssey.

Wikipedia, MobyGames, OGDB, IGDB

https://www.youtube.com/watch?v=KIclrtLnoQs

#2 - Hint

It actually made me think of another quote, though different it had a similar impact, from the movie franchise this game's a part of, where a certain someone says he is a certain someone's relative.

Sonic 2006?

#3
Hint 1: Bring the key to the door.
Hint 2: Barrels.

#2
Hint 1: The only mainline game from one of my favorite franchisises that isn't on my list yet.
Hint 2: It's not a Zelda game.

honorable mentions

Getting a place in my TOP 50 was a fierce competition. I considered more than 80 games. All of these are great, but there were only 50 spots under the sun. So some honorable mentions. I left out more Etrian Odysseys, Zeldas, Baldur's Gate 2 or stuff like that, only mention some games that are different to what made my TOP 50.

Wii Sports Resort (Wii, 2009)

Yeah, I do like casual games like these, if they are made well. I was a fan of Wii Sports, and this game built upon the base and offered just more of it. Only I wished Tennis would've been included too.

Dune (DOS, 1992)

This game had first real-time tactical combat, that evolved into Command and Conquer and over the time into Warcraft and Starcraft. Still Dune is more of an classical adventure game, and a good one at this.

Hearthstone (Android, 2014)

I like trading-card-games (I liked Magic The Gathering back then), so Hearthstone is just up my alley. The gameplay is good, the variety good enough and you have a lot to collect.

Chaos Overlords (DOS, 1996)

Fight for control over the city by controlling areas, bullying local businesses into obedience and recruit gangsters, punks and others to take over more of the city, until you meet a winning conditions. There is a big choice of possible winning conditions and your enemies can be played by computer-AI or friends at the same computer (the game is turn-based, you switch control).

Dillon's Rolling Western (3DS, 2012)

Seldom I had so much fun with a tower-defense-game. This game is cute, creates a lot of challenge in harder levels and is a blast to play.

Micro Machines (DOS, 1991)

Micro Machines had a simple yet captivating gameplay: Drive a competitive race with small cars on the table with normal daily items as obstacles that mark the course and win. The gameplay was brutal. All racers were on one screen, who was to slow to fall off-screen was out. This was a blast to play with friends.

Bravely Default (3DS, 2012)

Bravely Default had great ideas to develop further turn-based combat options. Add to that cute looks and funny dialogue and you have a great RPG.

Duke Nukem 3D (DOS, 1996)

Aliens invade earth and mutate people, wreaking havoc? What to do? Enter the Duke, he can solve this. With a lot of explosions, funny cutscenes and sappy comments. Probably the only game in which you shoot an alien that sits on the toilet.

Is #3 Doom?

I know this is a Star Wars game I haven't played.  I am going to guess Knights of the Old Republic, since I know a lot of people really like that one.

Yes, this is real time combat with 4 characters in a fashion like Baldur's Gate.  Of course you are super heroes instead of D&D characters.  And you don't have an overworld map like a D&D game.  Instead you have mission areas, and then you advance your character's abilities in between the missions.  There is tons of replay value since you can focus on a different group of characters every time you play this game.

Does it matter what order I play these games in?  I am very likely to play one of the Etrian Odyssey games in 2018.  I just finished replaying Final Fantasy 1 a month or so ago.  I have always really liked it, but I also feel it is showing its age in a lot of ways.  I also will sometimes play a roguelike game like the various Mystery Dungeon games, but I think what I am really after is an old school dungeon crawler that has made gradual improvements over the years.  Something like Wizardry or Final Fantasy 1, with maybe a few updates while maintaining most of the old school feel.  

I am always looking for a good tower defense game on a console, and somehow I've never heard of this one.  (For some reason game developers think Tower Defense is mostly for flash games or mobile only.)  I might have missed this game because it is download only.  This is one I'm definitely going to check out.

Nope, it's not similar to Doom at all.

Yes! That is correct!

I don't know if you know what my hint referred to, so I'll keep that spoiler to myself.

#2 Etrian Odyssey IV Legends of the Titan

Edit: Mods stop shrinking my images. They are no larger than anybody else's in this thread. If you continue to do this I will report you to site leads. 

Turn based JRPG combat has a lot of potential, but most developers just don't take this combat engine to it's fullest. Real challenges aren't ever presented to the player, because the developer hasn't added enough complexity to give the player more than one option. Beating a truly hard enemy in a JRPG usually comes down to using the same OP tactic. There's no room for finesse or being original. The Etrian Odyssey series changes all that by *gasp* allowing you to do to the boss anything you can do to a regular enemy. Normally bosses resist status effects like crazy in JRPGs to the point where using them is a bad strategy. But in Etrian Odyssey bosses can be... Poisoned, given concussions, turned to stone, tripped, tied up, paralyzed, confused, blinded, and much, much more. Now, I know what you're saying. That sounds like the bosses would be too easy to beat. Yeah, well EO bosses deal a ton of damage, can inflict the same status effects on you, and usually come with a downright devious twist. Oh? Did I mention that bosses don't wait for you to fight them in this series? Bosses actively hunt your party down. Movement in this game is grid based, and everytime you move bosses can move as well. When you are in combat each turn you take let's the enemy boss move closer to you. So you can sit there in a fight with normal enemies and suddenly a super scary boss (that you weren't really ready for) finds you! 

EO IV gets the top spot in the series for multiple reasons. First off, this entry introduces cross classing. Each character has a main class, and a secondary class. You get access to exactly half the skills in your secondary class, as you get in a main class. So if you go Ninja main, and Black Mage secondary, you can only level up your Meteor to level 5/10, but can level up your Ninja Stars to 10/10. Anyway this leads to combinations that would normally be super OP, but not in an EO game. EO IV also has an open world that is explorable in an airship, unlike previous games, and it was the first EO game to take the series from lazy unanimated 2D alphamaps to full blown 3D. Finally the music in this game is just a cut above the rest of the series. 

Oh, and I'm quoting Mnementh here because almost everything he says about EO Untold applies to EO IV as well. 

Excellent choice for #2. I'll be picking up EO Untold sometime next year. Have you played EOV yet?