Your specific question about reliability probably depends on the geographical region you are sending to. Hopefully more devs can offer real life experience. Twilio does have a big user base and usually this suggests the service is good http://techcrunch.com/2012/06/05/twilio-passes-a-milestone-100000-developers-for-its-voip-sms-platform/
Also see this previous SO entry https://stackoverflow.com/questions/2528919/sms-gateway-service-provider-with-php-api
Choosing a provider does also depend on what countries you require coverage for, whether you require the ability to send and receive, and if you want a dedicated shortcode.
There are a whole bunch of companies offering web based APIs for sending SMS including a bunch of operators offering a service. These tend to offer different international coverage with most having the best coverage in particular regions. The cost of the services also varies with setup fees varying between companies and depending on if you require a dedicated shortcode set up.
Here are some of the better known companies offering SMS web API services
Twilio - US coverage for send and receive but currently running an international beta program https://www.twilio.com/international-sms, no setup fees or minimum contract for the standard service however there is a 3 month minimum if you want to use a short code.
Tropo - US coverage for send and receive and it is possible to send SMS message to international numbers but not receive.
Zeep - US only coverage and send only, with a minimum monthly spend and using a Zeep shortcode.
Nexmo - No setup fee or minimum monthly fees. Provides international coverage with currently a low rate on SMS sending in the US. Limited country coverage for receiving SMS.
MediaBurst - UK based company with International coverage for send and receive SMS APIs. Note that "international coverage" does not necessarily include all US carriers (for example) but the majority. They give a fixed price of £0.05 per SMS with bulk pricing. Does not seem to support custom short codes.
There are also some operators offering web based APIs for sending SMS through their network including:
Bluevia offer a unique profit share model where the developer shares the profits of the sent (or received) sms, however the coverage is limited to Telefonica networks in some European and South American countries (see https://bluevia.com/en/page/tech.overview.countries). They also offer payment and location APIs.
The recently launched OneAPI is available on the three major operators in Canada and is to be rolled out to different countries soon. This gives access to sending and receiving SMS as well as some other things like payment and location. The cost for sending and receiving SMS depends on the operator.