Any system that requires transactional email message functionality as an external service. The benefits of a well managed and vetted server to maintain reputation as well as being reliability is well worth the effort needed to integrate towards the API specs
SMTP Email Relay Solutions is a great service if you are in a field where sending out bulk information, such as monthly statements to clients, invoices, or any back-to-back emails that would normally get flagged for "spam" is required.
Mandrill is extremely reliable. We switched from using a platform that was very hit-or-miss, but we never had a single deliverability issue with Mandrill's transactional API. Every email was sent reliably and quickly.
Mandrill's reporting and debugging features made it easy to ensure that all our messages were getting delivered to the right place in a timely manner. In fact, Mandrill's tools were so robust that we used it as an end-around way of debugging another failing service we were using.
Mandrill is a very affordable add-on to an existing MailChimp account. Adding an extra layer of reliability was a no-brainer, and made the cost essentially negligible to our organization.
The rate-limit system can be troubling. If you are switching providers and already have a large e-mail volume, you're going to want to transition slowly. The per-hour send limits are initially very low, and if you have any deliverability or complaint hiccups, they will plummet quickly. The Mandrill support staff is very helpful in this area - they will not (and claim that they can not) manipulate send limits for any account at any time for any reason.
Billing is combined in with a paid MailChimp subscription, which didn't used to be the case.
It did the job for us and we were happy with the delivery rates of the email, analytics and customisation available while integrating it within our platform.
I haven't personally reached out to their support team, but the feedback I've heard from our tech support and engineering teams have been that their response to questions has often been they either are unsure or that Mandrill is what it is. For example, when our customers weren't able to see opens and clicks for all emails sent, and we reached out to their support, the response was it is what it is, and they'll send a notification to our app if they can.
So we actually work with clients across all of the platforms listed above, but Mandrill has a huge ease of use bonus in its favor, especially when working with clients who are setting up a Cart Recovery style marketing campaign for the first time or are looking for a bit of a fire-and-forget setup. With more sophisticated clients (on the scale of global ecommerce companies), who have a larger subscriber/customer base and in-house design teams, we find that Mandrill usually isn't enough
Office 365 does use secure non-standard ports for SMTP connectivity causing a problem with older programs. SMTP Email Delivery from Exchange solves this problem by giving the network admin full control over ports and specific program connections. While we do use both Office 365 and the SMTP Email Delivery we find that a mix is needed in order to meet all expectations for our end users. The majority of our SMTP communications, for users, go through Office 365 while the majority of our applications and servers do go through the SMTP Email Delivery service.