Just like all other sports, baseball has a lot of video games for consoles, PC and smart phones. The most popular is MLB The Show, but it's available only on consoles - PlayStation and Xbox and Nintendo Switch.
MLB The Show
PS2/PS3/PS4/PS5, Xbox One/Xbox Series X/S*, Nintendo Switch**
* – since “2021”; ** – since “2022”
This game is, in terms of features and overall quality, similar to PES, EA FC, NBA2K and EA NHL. It is a baseball simulation with all MLB teams and minor leagues - AAA and AA. The most popular single player modes are Franchise and Road To The Show. For online play, there are lot of different modes, the most popular is Diamond Dynasty (which is similar to EAFC's FUT).
In Road To The Show you can create your own player and who will be drafted to a MLB franchise. After the draft, you will begin your journey to the majors. You will start in AA and from there you will, hopefully, be promoted to the MLB team.
On “next-gen” consoles, you can create your own stadiums and use it in the Franchise mode.
MLB The Show is developed by Sony's San Diego Studio and for long time it was a Sony exclusive. Starting from 2021, this game is published on other consoles as well.
MLB 2k12
PS2/PS3,Xbox 360,PC
Since there are no new baseball games at the market, MLB 2k13 is still the latest one for PCs. While 2k13 is the latest, 2k12 community is huge and there are plenty of mods online so it's better to get that one. You can get a lot of mods on https://mvpmods.com.
MVP Baseball 2005
PS2,Xbox 360,PC
MVP Baseball 2005 is a twenty years old game, but it's one legendary baseball game and the community is huge. Also, this is the last MLB game released by EA Sports. For season 2006, TakeTwo Interactive (MLB 2k) obtained rights for MLB. EA Sports relased one more baseball game, but it was college baseball - MVP 06: NCAA Baseball.
MVP Baseball 2005 has advanced franchise mode as well as some other modes such as Dynasty and mini games.
Super Mega Baseball 2/3/4
PS4/PS5,Xbox One/Xbox Series X/S,PC,Nintendo Switch
This is an arcade baseball game and it's not licensed by MLB but, in all honesty, it doesn't have to be. In the game you can either use existing teams or create your own. All players are cartoonish, but it's very fun to play and there is the franchise mode.
Out of the Park Baseball (OOTP)
PC
If you like Football Manager series (soccer) - you will like this. You are a general manager of your franchise and you deal with advanced stuff such as scouting, training, roster control, trades and so on.
MLB 9 Innings
Android,iOS (iPhone)
For smartphones (Android and iOS) there MLB 9 Innigs. There is franchise mode and for online players, there is mode similar to "Diamond Dynasty".