App limit on a single Heroku account

There's currently no limit on the number of apps that you can create, but please see item 4.4 of the Heroku Terms of Service.

You may not develop multiple Applications to simulate or act as a single
Application or otherwise access the Heroku Services in a manner intended
to avoid incurring fees.

A clear answer surfaced in the Heroku July 2013 newsletter about platform limits. The maximum number of apps per account is 100.

Reference: https://devcenter.heroku.com/articles/limits#maximum-number-of-apps

Unverified accounts can create at most 5 apps. Verified accounts can create no more than 200 apps.

Source: https://devcenter.heroku.com/articles/limits#maximum-number-of-applications

PS: To verify your account you'll need to provide a payment method (credit/debit/prepaid card).

If you have unverified account then the maximum number of apps is 5 only and for verified account number is 100.