I'll split this answer into two parts:
Email Validation in terms of double opt-in
Email Validation in terms of actual real-time verification using a web service / API
In my opinion, the practice of double opt-in is advisable when
- email is one of the most important means of communication between your business and its customers
- sensitive data (e.g. invoices) are being sent out via email
- crucial service notifications/announcements are being sent out via email
- if your product/website generally tends to attract spammers/abusers
If, however, your website does not make any special use of customer email addresses and relies on a system of simplicity, I'd skip the double opt-in, or at least rethink it, since it is one more step the user needs to take before being able to use your service (a matter of UX)
- As to the use of real-time email validation on the back-end, in my opinion, every business should verify email addresses in real-time via an API.
For the simple reason that is mostly free (Free, Powerful Email Validation API), it verifies the actual existence of an email address, checks for misspellings and typos, checks for free & disposable email providers, and it does not require the end-user to do anything.