How does higher mathematics or theoretical physics effect the personal lives of those who study those topics? Studying such fields contributes to the overall advancement of humanity. The students, as members of humanity themselves, are effected, even if infinitesimally, by the overall advancement of human knowledge.
The same applies to philosophy: Philosophy is a wissenbchaftwissenschaft, a from of seeking knowledge and wisdom, and as such contributes to the overall advancement of human knowledge, and it effects the personal lives of those who study it in the same way that mathematics or theoretical physics does.
There are more prosaic ways of looking at the question though: Ask anyone living in an oppressive theocracy whether the question of God's existence effecteffects their personal lives or not? Ask anyone living in a communist country whether Marx's ideas effect their personal lives or not? There answer will be a definite "yes, philosophy sure does effect our personal lives!", presumably this includes students living in these situations.
Finally, someone had already pointed out in this forum - I forget which post - that although we now consider Socrates, Plato, Aristotle, The Stoics and the Epicureans, and their ilk, as semi-divine mythical sources of wisdom, those guys were really just the self-help authors of their times, simply offering people advice on how to improve their lot in life. Any student of philosophy in our time is free to take their wisdom as such as well.
Personally, I am an amateur student of philosophy myself (no formal training except for a couple of high-school classes). Coming into contact with analytic philosophy has definitely changed the way I look things, and more importantly the way I argue and negotiate with people, in both my personal and my professional life.