Flicky (Sega Genesis, 1984)
Most kids that owned a Sega Genesis or bought any of the few Genesis Collection games that came out on modern consoles probably know of this game. The object of the game is to travel around the looping house as a bluebird, capturing little chicks and saving them from cats, which can be easily defeated by throwing random household objects at them. The game is probably one of the most cutesy games of the classic era, but definitely not the most challenging. One could play for hours just running around the map and saving baby chicks, and the minigames are just as addicting. The game does get challenging when you reach higher levels, but for the most part, it's a lot less stressful and a lot more relaxed than most of the other mainstream Genesis games like Sonic the Hedgehog and Comix Zone.
Rollcage (Playstation, 1999)
This hidden gem of a race gaming from the PS1 is pretty simple when it comes to gameplay, but interesting when it comes to the many worlds and modes the game has. You can race in your "armored RC car" (as I call it) on several tracks, ranging from a beachfront track to even Mars. YOU CAN RACE PEOPLE ON MARS. The graphics, though aged and basic now, are pretty stellar for the time, depicting Mars in a very vivid way. You can race against other racers or time attack. I usually just choose a time attack and one of the tracks on Mars and just go for ages, just relaxing and checking out the scenery and cool tunnel mechanics. The only con to this game: none of the racers are flawless. Even the all-around choices occasionally spiral out of control. However, the game poses no real challenge and is quite relaxing to the eyes. Or I think so at least.
RC Stunt Copter (Playstation, 1999)
This game is basically just as the title suggests. You can choose to fly a remote-control helicopter of any difficulty around your choice of level in your choice of mode. There is a training mode and challenge mode for those seeking to move forward, but there is a Free Flight mode that lets you choose a map or area and just goof off. The best part? Every area has its own little perk. Your copter turns into a dragonfly at the pond, you can shoot balloons with your copter at the theme park, and you can even fly in two different space worlds. Aside from the gameplay, the music is also quite relaxing. The pond music is light and smooth, the farm music is light and bouncy, and the space music is classic. This game, though not as active as Crash Bandicoot or any other mainstream PS1 game for that matter, had a unique style with underrated developers. I know I've spent literal hours just flying around the different maps and doing different tricks. As well as crashing copters over and over again. That's therapeutic too.
Asteroids (Playstation, 1998)
This game is just what you'd expect it to be: a modernized re-vamp of the classic arcade game of the same name. To me, this game was always quite relaxing. Just sit in the middle and make sure no asteroids crash into you. It's fun to just pick them away with not a lot of care. I also like the backgrounds of the different worlds. The artists for this game were really imaginative when it came to playing with the backgrounds.
Worms Armageddon (Playstation, 1999)
This game, though also on Steam if I did my research right, was originally a classic game for the PS1. For those who don't know the game, you play as a team of worms with a variety of weapons in a turn-based war zone. Aside from average gameplay and multiplayer, you can literally just choose four players in the multiplier menu and, if only one controller is plugged in, you play as all four of the warring teams. It's actually really fun and relaxing to blow things up and random, not caring who you hurt in the game because you control everyone. I don't know if it's the same for all games or if mine's bugged, but it's definitely a neat little aspect that makes the game all the more fun and funny for me. Mindless violence. Golden, isn't it?
Toy Story Activity Center (PC, 1996)
Just like every other Disney Activity Center game, this contains many different games for us computer-savvy toddlers to play around with. However, this one seems to have more games than the rest of the Activity Center games. You have a choice of three areas to visit where you can do more challenging things like solving puzzles or testing memory, but there are some pretty creative games as well, including marble art, making toys out of spare parts, and putting different sounds together. The game is just a relaxing, nostalgic walk through my childhood, playing fun games with the Toy Story characters. What kind of 90s kid doesn't appreciate that?
Humongous Entertainment Junior Arcade series (PC, 1996 - 1999)
For those who were almost religiously addicted to their computers at a young age like I was, these games are pleasant trip back to simpler times. The Humongous Entertainment games were all games for younger kids, sometimes sending the main character on adventure and teaching lessons all along the way. These arcade games were like spin-offs with one of the main character in each of the Humongous adventures leading the way. You could play for hours through easy and fun levels as well as make your own in most of the games, performing unique tasks each time. From sorting socks and popping bubbles to getting lost in mazes and collecting lost items in the woods, the different mechanics in each were all fairly fresh and unique. I think these take me back more than the rest even.
The Sims series (PC, 2000 - present)
Now, this is probably the most recent of titles you'll see on this list. However, this did start right along with the new millennium, so it's already a 16-year-old series. Most everyone knows The Sims is just a living simulator. You can make unique people and houses to live with and in. It's actually kind of relaxing to take a break from your life to control someone else's, metaphorically speaking. You can even let them wander free and get into trouble. This game's just as calming and therapeutic WITHOUT removing the ladder from the swimming pool while your Sims are swimming. I see you smiling out there, random citizen.
Sky Odyssey (PS2, 2000)
MTV Music Generator 2 (PS2, 2001)
A lot of people actually file this game as rubbish, but I think it's still pretty fun to mess around on. This is game was one of the first music-making type of games for the console. Compared to today's standards, it's just a more complicated version of Garage Band or a severely basic version of Fruity Loops, but for it's time, it wasn't too bad. It was one of the first of its kind for the console, and the Gorillaz even recorded a song on it for the common consumer to hear. That's nice easter egg in addition to the general music-making.
Grand Theft Auto: San Andreas (PS2, 2004)
Everyone who's reading this list right now probably knows exactly how it feels to be playing this game with big books of cheat codes (or notebook paper with cheats scribbled all over it) right next to you. No one really plays the mission mode in this game if they have an unlimited access to the cheats. You can get any weapon, any vehicle, and many special abilities, both cool and ridiculous. Plus it was just fun to explore the world, goof off, and do stupid things. This game now might be overshadowed by the 5th installment of the series, but us classic gamers remember these old days. For those who may have never experienced the power of the cheat codes (or for quick access), find them at the official website!
FlatOut (PS2, 2005)
Those who are remembering this game now are probably having a good laugh about all of the stupid stuff they were able to do in the game. The crashes in this game were so wacky, the developers decided to add a challenge-type mode in addition to the normal racing mode. These challenges were really just funny things you could do in crashing to get a better record score. One of the ones I remember best was speeding down a ramp and pressing a button to launch my driver out of the car and into a net. The higher my character stuck on the net, the better my score would be. Ahh, good wacky times.
Star Wars: Battlefront II (PS2, 2005)
Most people probably remember this game and may not even consider it old enough to be classic, but it's definitely fun to goof off to if you play the right mode. If you go to the Instant Action menu, you can create a sort of playlist of all of the different levels. Including both space battles and planetary invasion, the player can go on for hours playing through the different maps and modes. One of my favorite modes is the "Assault" mode on the Mos Eisley world. Those who know what I'm talking about are already smiling. For, in this mode, you had a choice between the popular heroes and villains in the series, ranging from the likes of Luke Skywalker and Obi-Wan Kenobi to the likes of Boba Fett and Han Solo. Even a few of the lesser-known Jedi are added into the mix, including Aayla Secure and Ki Adi Mundi. Gosh, I spent hours on this mode. (Also available for Xbox, if I'm correct)
Bully (PS2, 2006)
Hey, look, another game from Rockstar on this list! (San Andreas) In all seriousness, this game isn't really a goof-off type game at heart. Bully has one of the best stories of the PS2 era and the player almost wishes it wouldn't end when the game is over. This is where the goof-off part comes in, for the developers added in an "Endless Summer" mode after you beat the game. This allows you to browse the world continuously, getting into trouble as you wish and even going back to collect items you missed or complete missions you forgot. I have spent literally years playing on the Endless mode and I haven't gotten everything. And it's still fun. In addition to the main game, you can also go back and play any of the arcade games at the main character's various different hideouts/save points in the town. For a story-driven game, the replay value is quite rich.
Well, I'm afraid that's all I have to add to this list. Keep in mind, this is based off of the games of my childhood and I'm not intending to list every game and reflect everyone's opinion. So, by all means, leave me a comment of what games or game modes were classic, relaxing, and pointlessly fun to you. Expand upon the list, if you will. Thanks for reading, and stay tuned for more obscure lists for the listless!