Friend without bank account wants me to deposit a gift check in my savings account. Will I be taxed for it or have other implications?
The short answer is "no". Gifts below $14K are not subject to any reporting requirements (assuming you are in the US).
The long answer is a series of questions: Is this person well-known to you? Why aren't they using the money to open their own bank account? Do they want you to give them cash right away, or are they willing to wait until the check clears? Which is all to say that this sounds slightly fishy. Be careful you are not inadvertently participating in a money-laundering or fraud scheme.
The simple answer is "don't do it." He should take the check, open a bank account, and after it clears, he'll have his money. I'm not suggesting that this is some kind of scam. I'm sure that every day lots of unbanked people get $10,000 checks and friends are happy to clear those checks. But on the rare chance the sender of that check is untrustworthy, or simply overdrew their account, why risk this?