I am an SMS newbie so
We've used mBlox (http://www.mblox) in the past, as they provide comprehensive international coverage, premium SMS, various levels of Quality of Service vs Price, and a solid Java-based API for both inbound and outbound SMS.
TextMarks provides a service where they map an incoming SMS to them to an HTTP GET to a URL you provide and then send the response back as another SMS. They don't charge you if you let them add some advertising to the reply SMS. The problem is they don't provide this for free anymore for T-Mobile due to T-Mobile charging them. I'd be willing to pay per message, but they charge $0.20 per user-month, which is rather steep. Anyone know of anyone who provides this service?
First, you need an SMS gateway. Take a look at Kannel SMS Gateway.
You might take a look at Gammu if you're running on a Linux box:
http://www.gammu.org
Using Gammu, you can configure it to periodically poll a mobile phone for new SMS messages. When Gammu finds new messages, it can store them in an SQL database. You can then write another program to periodically poll the database and take action on new messages.
Using this general setup I successfully deployed a homemade 2-way SMS application. I configured Gammu to pull messages off of the phone over Bluetooth. Gammu placed them in a MySQL database, which I had a Tomcat web application periodically poll for new messages. When a new message was found, the system processed the message.
This is a somewhat "duct-tape and bailing wire" setup, but it worked quite well and was more reliable than many of the "professional" SMS gateways I tested beforehand. YMMV.
I'm not up with Java, so here's a nice guide on how to do it in Ruby on Rails: http://www.lukeredpath.co.uk/2007/8/29/sending-sms-messages-from-your-rails-application
If you want to send 'true' SMS you'll need to use an SMS gateway, (use of one is outlined in the above guide).
You can use MMS to send messages, to an email address that looks something like 1234567890@ messages.whatever.com. You can use mail functions to do this. There's some information about that here: http://contentdeveloper.com/2006/06/open-source-sms-text-messaging-application/
You will need an SMS gateway, googling "SMS gateway" will reveal many. I have used http://www.clickatell.com/products/sms_gateway.php with great success.
I do not know of any open source implementations, but will be monitoring this thread in case someone else does!