There are some of the sites who let you send SMS without opening an account and giving your mobile number. One site I have reviewed previously is SMSti.com, you can send SMS and you will not be asked to provide your mobile number. But it is not in working condition. I tried this service to send SMS to some of the friends mobile but no SMS received never and this service always told SMS sent successfully. However, in past this service was working, but online anonymous SMS was never practically possible. And many other services were working but now you will not find any working service. And I believe these services should be closed.
Online tools like IP address tracer can easily detect your location and other details.
Why people search for anonymous SMS service? Because they want to send abusive SMS or threat someone anonymously, he can use this service for anonymously.
What you will get to read on SMSti when you go to send an SMS.
NOTE: Abuse is strictly forbidden. This service is NOT anonymous. We store all records and co-operate fully with the legal authorities to TRACE Abusive messages to the originator. Read the Terms and Conditions before you send your message.
You will not find a single SMS service who claims to be working anonymously anymore.