Video games can be one of the more difficult hobbies to go back to and enjoy older works, as it can sometimes require older hardware or hard to obtain older games. These days, it's a bit easier to get into retro gaming, in large part thanks to the increased popularity of retro handhelds, which put emulators on handheld devices to make emulation more accessible. Of course, the definition of what counts as retro gaming isn't universally agreed upon, and it largely depends on your age. You may draw the line in 3D or the year 2000, but the general rule seems to be anything more than 15 to 20 years old counts. You may not like hearing it, but that does mean that there are Xbox 360 and PS3 games that count as retro, although this list consists of games a bit older than that.

Related
6 retro classics I can easily emulate on my PC
From Chrono Trigger to Tekken 3, these retro gems still shine — and they’re just a few clicks away on your PC.
5 Super Mario Sunshine
Some people forget that being the worst 3D Mario is still better than 99% of games
Released in 2002 for the Nintendo GameCube, Super Mario Sunshine has a bit of a bad reputation. It's widely considered the low point of 3D Mario games, but playing it over 20 years after it released, it holds up so much better than other games. Yes, it still has some bugs and the pachinko level continues to be a nightmare, but the core design is still excellent. Not only does each location on Delfino Island get used in interesting ways, like the hotel casino area serving as the boo house level, but what stands out most is the cohesion.
Super Mario Sunshine has a cohesive island-theme and focus, with a plot revolving around graffiti and tourism, and while none of that is particularly deep, the island vibes are immaculate. Plus Metal Mario is sick to look at and F.L.U.U.D. holds up as a 3D Mario mechanic that works well.
4 Harvest Moon: Magical Melody
One of the best Harvest Moon games

Source: Marvelous Interactive
While we are living in a world where Stardew Valley is the best cozy game around, and it has inspired a new wave of great farming sims, it's still worth checking out some of the classics that inspired it. One of those is Harvest Moon: Magical Melody, which was released on the Nintendo GameCube in 2005. It has all the classic features: a farm to grow and sell crops, a barn to raise animals, fishing, and mining, as well as a wide selection of townsfolk to befriend and even marry. What makes this one special are two things: the first is the chibi art-style, which helps it be cute in addition to being cozy.
Second is the music note system. One of your main objectives is to free the Harvest Goddess from her statue prison, which can be done by acquiring enough music notes. These are awarded basically as achievements, marking milestones or accomplishments you have achieved. This gives an easy path to understanding what you should be focusing on, while also providing clear and simple rewards for completing those things.

Related
My 5 favorite GameCube games that Nintendo should add to NSO
Nintendo needs to add the GameCube to NSO and these are my favorite games that I hope get added first.
3 Diablo 2
Dungeon crawling action without the baggage

Source: Blizzard
A classic even in its own franchise, Diablo 2 is still the preferred dungeon crawler despite releasing back in 2000. While there are two modern iterations, Diablo 3 and Diablo 4 you could play, Diablo 2 offers a hardcore dungeon-crawling experience less bogged down by modern live-service elements. While ladders still exist, and the remastered version also includes them, a lack of a forced meta and constant balance changes means you can build your character how you want. It is also a difficult game and features less direction than the modern versions. Not only do the character-building and loot grinding still hold up compared to modern games, age hasn't taken away from the great game feel Diablo 2 still has.
It also isn't burdened by the older hardware it was made for. Not only is there a remastered version on modern consoles and PC, but you can still get the original for PC via Battle.net and the odds are pretty good that your current PC can handle a video game from the year 2000.
2 Pokémon Fire Red
Yes, the remake is old enough to be retro
Video games have been around long enough that some remakes are old enough to be retro games themselves. One prime example is Pokémon Fire Red, the Game Boy Advance remake of the original Pokémon Red. This version features color, some added content, and minor improvements that the series saw in generations after the original. It's also one of the purest forms of Pokémon you can experience. It still has a bit of bite when it comes to difficulty, and it doesn't have full-party EXP share, something controversial in newer Pokémon games, depending on who you ask. If you enjoy grinding in turn-based RPGs, this classic experience will be appealing to you, in a way that modern Pokémon games not only moved away from, but many don't even feature the option to play in the classic format.
The only downside to Pokemon Fire Red is that getting an authentic copy of the game for Game Boy Advance can be quite expensive, and it can be hard to tell a fake from an original if you don't have the knowledge. That said, it's fairly easy to set up a Game Boy Advance on a PC or phone, in addition to the many handheld emulators you can buy.
1 Paper Mario: The Thousand-Year Door
You don't need the new version
I understand why you might want to pick up the Nintendo Switch version of Paper Mario: The Thousand-Year Door, but you don't need to. Not only does the original 2004 GameCube version hold up incredibly well today, that version runs at 60 FPS, and the new version only hits 30 FPS. The fresh coat of paint isn't worth the $60 price, when you could just as easily play the original GameCube version.
Paper Mario: The Thousand-Year Door is also widely considered not only the best Paper Mario, but the best Mario RPG. It has an excellent cast of supporting characters with genuine personalities, sharp and funny writing throughout, and an active turn-based combat system that doesn't slip into gimmick territory the way modern entries have. GameCube emulation is in a great place too, although if you want to play this on original hardware, a physical copy of the game can be quite expensive, making the appeal of the Nintendo Switch version that much more apparent.
Retro games are easier to play than ever
While the need of original hardware is becoming more and more a luxury instead of a need, retro gaming has become easier than ever to get into. Not only do emulators work well on most modern PCs and even phones, without much work required, there are also numerous companies making retro handhelds, some of which come with games already installed. Game stores like GOG are also making these games more accessible for anyone who wants to legally own these classic games. Even if you aren't nostalgic for this era, plenty of classics are still great to play today.