If you encounter a game crash indicating that “Don’t Starve Together has run out of memory and must shut down” this typically is due to two things:
1. Your computer does not meet the game’s minimum system requirements, specifically for graphics memory.
Computers with graphics cards under 256 MB dedicated RAM will experience intermittent crashing issues as Don't Starve Together requires graphics cards with dedicated RAM of at least 256 MB or over.
Also please ensure that your computer surpasses the memory requirements if you are hosting a server or running a dedicated server. Check out Don't Starve Together's system requirements here. (If the computer falls below any of the listed system requirements, it will not be able to run the game properly.)
If your system is close to the threshold of supported requirements as listed in the link above, you can try enabling "Netbook Mode", Small Textures, or lower the screen resolution in the game's options menu to see if those help alleviate the issue.
2. There is currently a faulty or out-of-date mod on either the server or client-side that is causing a memory leak with your game.
Please Note: All mods are to be used at your own risk! If you decide to download a mod for Don't Starve Together and hit a snag, we won't be able to provide technical support as mods alter the game's code and original design.
If you have mods installed and encounter the "out of memory" error, ensure that all mod files have been deleted completely from your MODS folder for Don't Starve Together on Steam both for your client and/or from the server itself. You can do that by going into your Steam folders for Don't Starve Together and fully delete the contents of your game's "Mods" folder. \steamapps\common\Don't Starve Together\mods\
After deleting the mod files, go to the Steam Workshop for Don't Starve Together (while logged into your Steam account) and unsubscribe ALL of your mods so that whichever mod that was causing the problem is not automatically re-downloaded to your game the next time you run it.
Once the all mods have been unsubscribed from Steam Workshop, verify the integrity of Don't Starve Together's game files on the Steam client, and launch the game once more to see if that resolves your issue.
If you have tried all troubleshooting steps and are still unable to play the game, please report your issue in the Don't Starve Together Bug Tracker with your logs and information for bug reports.