There is a limit, but if your device is newer, you shouldn't have a problem. However, for general purposes, we suggest that you don't have more than 400 crops and 400 plants. (Plants include flowers/trees/grass/etc.)

The reason for this is that the more items that the game has to "deal with" the slower the game will run, and on older devices, it will make the game crash, which will make the user power down and power up the device each time that happens. Often, an app crash will lose small amounts of progress in the game (depending on how often the crash happens and how bad it was).

I hope this answers your question.