If you can't pay a monthly mailchimp fee with your current model, then the model needs changing.
edit: Take heed of Patrick's "marketing evolution" strategies below and realize there are oh-so-many more lucrative things to be working on than coding a custom mailer.
Let's say, for the sake of argument, that you're a much much better engineer than I am and can duplicate MailChimp's functionality in a single work day -- 8 hours. Spiffy for you! You'll save about $100 this year, or whatever, and do a bit better running your software business than waiting tables, despite the fact that you're a kick-booty engineer.
Instead, you could evolve your app. I don't know how much you can get done in a day, but we've established that you're a kick butt engineer, so maybe you get a new feature done. Yay. But most of your users won't use the feature. Most won't even know you have it. (Instrument your new features, folks. It is depressing but invaluable to correct your intuition that you know what your users want. Nobody knows what users want. Users don't even know what users want.)
Instead of spending a day on the app, you could spend a day on your email marketing. For example, A/B testing subject lines for your lifecycle emails. (Or, if you've read my blog recently, building systems which will let you do that sort of thing on a recurring basis.) I am totally not an email marketing guru (one of my skills to work on in 2010), but everything I know about split testing tells me that if you aren't doing it yet you're missing a LOT of opportunities to eek 5 to 10% performance gains out of it. Which, when you're doing email at scale, means you make stupid amounts of money. And you get to keep the improvements forever, since they'll probably never get stale, rot, or require upkeep.
My one "Oh that just isn't even fair" suggestion with regards to life cycle email: putting stuff in the subject line that reminds your customer they actually have an existing relationship with you works very, very well. The easiest possible example of this is pulling their name out of your records and putting it there. A/B test if you don't believe me.
A more sophisticated variant is tying your email creative to your usage data. The particulars of that will change with your commercial offering and service, but here's an example for me: I send customers an email 24 hours after signup which thanks them for signing up and tells them how to log back into their account and use it. Currently, it has a static subject line which is pretty uninspired -- something like "Here's how to print your bingo cards." One thing I want to try is to have the computer inspect their account and craft the subject line to appeal to their interests, such as "Susan, don't forget your Baby Shower bingo cards" if Susan had started working on baby shower cards yesterday but not printed them.
Intuitively, that sounds like it is a heck of a lot more compelling to me than the old subject line. I can do an experiment like that for far, far cheaper than adding additional features to my software, and it will probably have a bigger impact on the bottom line.
If you're doing iPhone apps at the traditional iPhone price point, though, I don't know how any service which charges for a marginal email is going to be worthwhile for you.
Just really could not get over that damned chimp staring at me, talking to me, telling me what to do all the damned time, I guess. =\
They start off at Free! for < 100 subs, http://newsberry.com/pricing/standard-plans
http://www.cleverreach.de/frontend/index.php?flang=en
For preparation I handcoded an html-table layout with some css which I later turned to inline css using http://premailer.dialect.ca/ because other css gets stripped out by gmail and other web mail clients.
You have some evidence experience to back up your suggestion?
The way I look at it, might as well make the email a blog post (for Google juice, so future people who look for it can find it, etc) and then just use an RSS to email service.
That being said, depending on your volume and functionality you require, http://www.aweber.com is also an option to consider.