How many community service hours do I need to apply to Harvard?
Zero
I don’t need any?
Yikes, I’ve heard it 247.5 hours. No more, no less.
When you use the word need it seems like you’re asking if a certain number is required. Community service is not a requirement to apply to Harvard. Having said that all of these types of schools want to know how you spent your time during high school. Some folks worked. Some did community service. So played music. Some built weather stations and nuclear submarines (I kid) and some did all of the above all at once… but you’re asking what’s needed to apply and zero is the answer.
@apparently22 You won the nice person game. I couldn’t help myself 
Community service is a requirement in some high schools (and some courts assign it!). To reiterate, community service is not a requirement of any colleges, including Harvard. In fact, there is no 'requirement" at all for extracurricular activities, but they are still key to getting in. Harvard wants to assemble an interesting class so the interests and activities of those admitted will vary widely and generally show some depth over the high school years. Good luck!