Apparently we've been restricted (though packet filtering) to some arbitrarily small and untenable number of emails a day by some bankrupt ISP (and they say that's how it's always been chortle). We've been using our own mail server for the last 15 years, and only recently they've been giving us guff.
Is there a way for a legitimate business to email their clients, who really want to receive these emails, by bypassing the ISP? The way we've been doing it is by breaking up into 20 or 30 emails, but that gets complicated and requires a lot of manual labor by the receptionist, and unless she's really careful we wind up emailing lots of people twice.
So what are my options (Hosted Email, Lithuanian Proxy Server, Different ISP, not writing awful PHP that sends out zillions of emails and gets us blacklisted)?
Move to an ISP that supports the type of traffic you want to generate.
get vps / cheap dedicated server and set up smtp relay there. use alternative port for smtp [ in worst case even 443 although traffic you'll sent will be smtp ].
remember not to set up open relay - filter based on src ip addres - that would be ip address of your server at current isp. i'm doing this kind of set-up for mass mailing, mostly because ips of shared web hosting i use in one case are blacklisted.
Get some hosted email service that does what you want. Seems fairly straightforward to me.
Edit:
"Hosted email" means a whole spectrum of offerings, from the very simple to the very complex (hosted Exchange, etc).
If you're just looking to be able to send arbitrary SMTP to the Internet w/o running afoul of your ISP's deep-packet-inspection, you might be looking for something like the MailHop Outbound service from DynDNS.com. This service, as an example, lets you specify their SMTP servers as a "smart host" in your existing on-site mail server (letting you use a variety of destination port numbers, assuming your on-site SMTP server supports using non-standard port numbers) such that your existing on-site mail server delivers outbound email to the DynDNS.com servers, which in turn perform final delivery to the Internet.
As Richard West has pointed out in the comments, the Mailhop Outbound service, at its default pricing level, only allows 150 relays / day. You can purchase more relays / day as necessary, or you can look at other providers who might offer more relays / day or relays / dollar. Bandwidth isn't free, so you're going to find transfer limits of some type (bytes or relays per day, typically) with most providers.
There are a variety of providers out there that can provide this level of service. Be aware that none of them take too kindly to unsolicited commercial email, so be sure that you don't run afoul of their policies with what you're sending.
If you're just looking for the ability to do "mass mailings" you might be happier with one of the mass mailing services mentioned by other posters.
We use Constant Contact to do email blasting to our customers. It works wonderfully, has very detailed reports, and seems to be pretty inexpensive.
With that said, to avoid the problems you're having with your ISP, I would consider running your own mail server. Without knowing your company's IT infrastructure, I can't really make a good suggestion, but I'm partial to Microsoft Exchange. If you have a small business, look at running Small Business Server.
I recommend you look at MailChimp.
ISP's often limit how many recipients an e-mail message can contain in an effort to fight spammers.
Using a service such as MailChimp also provides you with a ton of analytics to see the open rate, bounce rate, etc.
This also provides your users with an easy way to opt of of receiving your e-mail messages.
I have setup my own linux mail server that sends direct to the internet. This seems to work fairly well. All my mail clients (windows) then has the linux mail server's internal ip address as their smtp server.
A good, hopefully easy but not necesarily the cheap solution would be to get a good ISP (as others have hinted at too). A business contract with a good ISP does not limit the kind of traffic you generate in any way.
Another solution, also good and will probably be quite cheap also, is to get a VPS (Virtual Private Server) where you most definitely will not have any limitation on the kind of traffic. This also saves you from having to manage a stable server environment (redundant power, cooling and internet access) at your company office.
Updated on July 7th, 2012
If your current SMTP mail server(s) does not support your email list size or sending frequency, there are some options.
For more information about options to send more email than allowed by the hourly and daily limits imposed by your ISP or mail server read:
Email Send Limits and Options.
For a comprehensive list of the hourly and daily email sending limits for the major SMTP mail server hosts, read:
Email Sending Limits for ISP, Web Hosting and Free Email Providers
Best regards
Tom O'Leary
Consider a Google Apps account. They're free up to 50 users, and reasonably priced thereafter.
Is it even moral to answer this question with a technical answer? If the person asking this question is not a spammer (and to be honest, that doesn't seem likely), then the information we provide would help any spammer googling for this information.