This question frequently arises on the VoIP/Asterisk lists, since it is a question that VoIP service providers often wish to answer - "How do I SMS-enable my VoIP customer numbers?"
In other areas of the world, SMS is much more easily tied into existing voice networks - in the UK (among others) for instance, SMS is possible over PRI connections, which enables "land lines" to send and receive SMS messages. Clickatell, the company referenced previously, is based in South Africa. Buying their service for delivery of SMS into North America means that your messages will be the past even been blocked by carriers. Users cannot reply to those messages, because many other companies are using the same short code return address. If you look at their website, you'll see that if you live in one of a few non-NA nations, you can buy an actual phone number (not a short code) which can be used for high-volume bidirectional communication via SMS.
Here in North America, we're basically out of luck unless you hack together a hardware-based SMS device, and even that may be not reliable since carriers explicitly state that their accounts cannot be shared, and a large number of SMS messages to/from a particular account may cause it to be disconnected without warning. It appears to me that carriers have taken the stance that SMS should be for infrequent messages between actual fingers (no automation allowed!) or via short codes, and short codes involve a significant amount of cost, configuration, and even arbitrary approvals from the carriers on the use of a short code. If you look at the form required for a short code request, you'll discover that it's not for generic use - it's geared entirely for ad campaigns.
A few years ago I tried searching for SMS-enabled SIP telephone numbers (DIDs) and found that there was a new service available, but the monthly price floor was pretty steep. I still have not met anyone actually offering the service, but I'm sure there must be resellers of it by now. It was Level 3, offering SIP trunks with DIDs on them. Another company, Syniverse, was then SMS-enabling those numbers in an exclusive agreement. Payment had to go to each company, separately. The costs per number to enable SMS were fairly low, and the costs for message transmission were fairly low, but the Level 3 minimum purchase price was quite high (imagine that you could buy a nice sports car every month with the "minimum payment".) I have no idea if this service is still available, or how successful it's been.
If anyone now has direct experience with a reseller or small distributor of this service, let me know - I'm still looking for a SIP-capable DID that can handle SMTP/SMPP/XML-HTML transmission of SMS messages with some decent volume (200-1000 messages per day.)
Here's a message in a thread from a while back on this topic which has some pointers: