I'm generally sick of managing my own e-mail server, but there are some applications I'm working on that will be needing to communicate with 3rd party users over e-mail. For things such as registration confirmation, alerts, and account recovery.
I've been impressed with Gmail for personal use, and trust in Google's ability to handle arbitrary volume of requests, but is this scenario suggested?
The only requirements that I know of aside from using a business account, is that the applications will need to talk to their SMTP directly and over TLS/SSL.
If you have decent alternative mail hosting providers you like that are as reliable and reasonably priced, feel free to suggest them.
The only issue I'd see with using Google's outbound SMTP service is that it's limited to 500 emails/day. I'm not sure what volume of email you anticipate sending, but that may be an issue.
One thing to think about, though, is that it's really quite easy to set up your own sending-only MTA. The painful part of roll-your-own email hosting usually is managing all of the user accounts, IMAP servers, etc. Things get pretty simple when all you need to do is send out from the server. In fact, if you're using a Debian-based distro (I'm assuming you're using linux, which perhaps isn't the case), the postfix deb package has a "wizard" that does 99% of this work for you.
If you want something that is Gmail like, but still want to keep your data check out Zimbra: http://zimbra.com
It is an all in one (mail server + mail client) mail solution.
It doesn't have that many bells and whistles in the free version, but you do get that AJAX interface.