Dropbox says that as of March 2019, "Basic" users, which is the free tier, can add their account to three devices. Dropbox users who already have their account attached to more than three devices can keep them linked, but there will be no way to link additional devices when over the three device limit.
There has long been a free tier for Dropbox users, with no restrictions other than available storage space. The new three device limit will make Dropbox's free service less appealing to users, though it could spur upgrades.
To get unlimited device syncing, Dropbox users will now have to upgrade to a "Plus" or "Professional" Dropbox account. Plus is priced at $9.99 per month for 1TB of storage, while Professional costs $19.99 per month for 2TB of storage. There are discounts available when purchasing a yearly plan, however.