A person who collects objects is called a "collector" or a "hobbyist." He may also be called a "compiler" or an "accumulator." The slang terms "pack rat" and "hoarder" might be more appropriate for people who collect everyday objects though these terms carry negative connotations.
Sometimes, an adjective is added before the word "collector" to describe what the person collects. For instance, someone who collects coins as a hobby may be called a "coin collector," while one who collects dolls is called a "doll collector." "Collector" can also refer to someone who has been hired to collect money from individuals for a company's debts, such as a tax collector.