How many hours of speech do kids hear before learning a language? I'd like some estimates of how many hours of English speech kids typically are exposed to before reaching various levels of mastery. 

I realize this is a very fuzzy question, but I'm sure ballpark numbers must exist. The motivation for this question is trying to get a lower bound for the required size of a training corpus for automatic speech recognition (ASR) systems.
Children, when they learn their first language, do not learn this language, rather they "learn the world". An adult spends some time of his day on learning a (second) language, and much time on other tasks. For an adult, the two (or more) activities are mostly separate. For a child learning a first language, learning this language is inseparably entwined with learning about what his perceptions mean and what his actions effect. It takes a normal child about 12 to 16 years to fully grasp the depths of his mother tongue, because a basic understanding of the world takes that long. And with "the depths" I do not mean all the words and perfect grammar, but a basic average ability to understand and express yourself in your mother tongue.

For a teenage or adult native English speaker learning a second language, an average of 575 (for "easy" languages) and 2200 class hours (for "difficult" languages) was estimated to reach a high level of proficiency (sources at Wikipedia). To this you have to add homework and self-directed learning for and after classes, so your overall learning hours will multiply. Numbers will differ for native speakers of other languages (because learning a language that is similar or even related to your own is easier).

(Do not forget that humans need time for knowledge to "settle". If you try to learn to much in too little time, the new knowledge pushes out what has not yet been "fixed" in your long term memory. So you need to spread these actual learning hours over several months or years, allowing for rest and active practise.)