The number of files you can store in your Dropbox is limited by the amount of storage space in your Dropbox account. If you run out of space in your personal account, consider upgrading to Dropbox Plus or Professional.
While you can store as many files as you have storage space for, you may not be able to sync all those files to your computer. The number of files you can sync to your computer is limited by your computer hard drive space. If you reach your computer hard drive space, try using selective sync or Smart Sync.
Number of files and desktop app performance
The performance of the Dropbox desktop app can decline if you have more than 300,000 files synced to your computer. This is a soft limit and depends highly on the hardware specifications of the computer running the app. Some customers can sync more files without issue.
If you have a lot of files stored in Dropbox and you'd like to try to improve the performance of your computer, you can use selective sync to select only certain files to sync to your computer. You can still access all of your files from dropbox.com or other devices linked to your account.
Note: This limit is related to the number of files, not to their size. Dropbox accounts with a large number of files may take longer to sync. A delay in syncing or a prolonged sync is not necessarily a sign of a problem. Adjusting your bandwidth settings may increase your sync speed.