I've noticed: É hora + DE; aprender + A; começar + A; ter (um trabalho importante) + A (realizar); ter (muito) + O QUE (fazer); saber (+ COMO --- sometimes); pensar + EM; ... and now - Não há tempo + A.
Is there a list of verbs and phrases that take 'something' before an Infinitive and where can we find it?
Well, I don't think it's gonna be so easy to find a list of these rules.
For example, here you have the prepositions used after some verbs starting with "a": http://solinguagem.blogspot.com.br/2011/04/regencia-verbal.html
It may help you. then you can look up the other verbs too as needed!
Prepositions is a hard predicament in every language.