This is a survival website, and I figure overall strength is more useful for survival than is being great in one exercise.  While 100 push-ups is a noble goal for motivating yourself, there are more productive ways to build strength.  Being able to say you can do 100 push-ups is mostly for bragging rights.  If you're like me, you care less about bragging rights, and more about overall strength.  
Nowadays, for strength building, I mainly do Grease the Groove, instead of spending large blocks of time in the gym.  Grease the Groove allows me to be more consistent.  My main exercises are push-ups, pull-ups and dips.  Once I reach a plateau, I inject a more difficult exercise variation.  For example, search "push-up variation" on Youtube.
For overall strength, I think it's better to workout with many exercise variations.  I have found this tends to make me pretty good in a lot of different exercises, and not exceptional in any one movement.  My maximums are about 60 push-ups, 16 pull-ups, and 35 dips.  I workout with different variations of these exercises.  I think that's pretty good overall, but nothing for bragging if we're considering the exercises individually.  By the way, I recommend Youtube for keeping yourself humble! 

I feel like I'm building useful strength more efficiently by focusing on variety.  I can also gauge my balance better.  For example, I feel like my pushing strength is disproportionately stronger than my pulling strength.  I'd like to increase my pull-ups to 20 reps max before I increase my pushing strength.