I have a friend and really want to play minecraft with him. However, he does not have an account. Can I play minecraft with him without buying minecraft again?
No, Your friend needs to have their own account.
This is made clear in the End User License Agreement:
The one major rule is that you must not distribute anything we've made. By "distribute anything we've made" what we mean is "give copies of the game away, make commercial use of, try to make money from, or let other people get access to our game and its parts in a way that is unfair or unreasonable".
I also answered a similar question recently, and obtained an official answer from Mojang support, which addresses this briefly:
There's bits of truth in various comments in the thread you've linked. The intent here is that we don't want people buying an account and then sharing it between friends, who should all have their own account. We've even seen things like sharing sites, where they basically rent out accounts, and that's definitely against the rules...
(emphasis mine). In summary, your friend must have his own account in order for you both to play together.
Do note that it would be considered 'fair and resonable' for you to allow your friend to play your copy at your house and on your PC - but giving them access to the account for them to play at their home when you're not using it would not be OK.