Most mistakes with apostrophes occur with pronouns, especially possessive pronouns. For example, the word for belonging to it is its, not it's. Also, the word for belonging to us is ours, not our's.
Apostrophes are not normally used to make plurals, and and you should never use an apostrophe to pluralize a word. For example, the plural of apple is apples, not apple's. The plural of orange is oranges, not orange's.