Can you get pregnant anytime during your cycle?

See answer. You ovulate 14 days before your cylcle, so if you are regular, you can have a good idea of when you ovulate. You are most likely to get pregnant mid cycle when you ovulate, so the week(s) around ovulation you are at the highest risk to get pregnant, and of course right at ovulation even more so. Unprotected sex right after your period and right before, your chances of pregnancy are very low.
Risk varies. You are maximally fertile during ovulation and this can sometimes be estimated by mittelschmerz (pain on ovulation). But there is a small risk even at the extremes (remember this is called vatican roulette).