Absolutely prayer works!
It's not all about asking for something, but I've seen (and been directly involved in) healing taking place through prayer - instantly. Intercessory prayer is just as quickly answered and physical evidence is before our eyes - again, instantly.
God *hears* all prayers, but he does not *listen* to all prayers (such as those of unbelievers***), which is an answer in itself, is it not? The Bible is crystal clear about the kinds of prayers God listens to and answers. The answers we seek aren't always delivered immediately, especially those involving 'The deeper things of God.' However, God *will* answer us when we are ready for the information. Rather like, or along the same lines as 'When the student is ready, the teacher will appear.' - Jesse.
*** Unbelievers truly *seeking* God are an exception to this rule. If one is seeking God for the purpose of knowing Him and not for some self-serving reasons, then God will reveal Himself through Christ and/or The Holy Spirit to those who seek Him but who do not yet believe.