iAlert.com provides SMS and email messages for weather alerts. The free account only lets you get alerts for one location, but you can choose what type of alerts, and whether you want to subscribe ($) for more than one location. (Disclosure: I have no affiliation other than being a user.)
I've subscribed before, listing Sprint as the carrier, but this sometimes works, and sometimes it seems like they rescan the number and it gets cancelled, though the email alerts continue.
I went through the process with them to add Ting, so now it is listed as a carrier at the bottom of the non-alphabet-ordered list.
The free account sends the SMS via the email-to-SMS avenue so might be delayed by a bit, and paid accounts receive them as a normal SMS, so might be faster.
I like the SMS option, since it provides coverage even when data is turned off or you're out of a data coverage area.