Which verbs take haben and which take sein in the past tense?

All verbs which indicate movement (or lack thereof) require sein. Everything else requires haben. For example, 'ich bin gegangen,' and 'ich bin geblieben' both refer to movement/lack of movement, which is why they take sein. 'Essen,' for example, does not make any reference to position or movement, which is why we say 'ich habe gegessen'.