I was so busy writing about peek vs peak that I forgot about a third word that sounds like these two, but is spelled differently and has an entirely different meaning:
Now granted, this is not an English word -- it's French. But it is used in English communications, so you may as well add it to the previous two as a group of homophones to which you should pay attention.
Pique: there are several meanings, but when used in American English, it's most commonly used with the word "interest." To pique someone's interest is to attract or excite them. Here's a link to Reference.com's definitions, along with the pronounciation.
I know it's doesn't seem fair to throw in a word from another language, but if you know your European history, the English and French were constantly changing ownership of the northern part of France. So it's not surprising that we find French words showing up regularly in our English communications. And the French have accepted a handful of English words in return, like "le week-end." Seriously: I learned that fact in my French classes....