It would be pretty hard for somebody to inadvertently send you a bitcoin.

if I got it for free, then I would not give it back. I think it was a gift for me because of the possibility of wrong delivery address wallet does not seem likely.

I doubt I would notice as all my btc is in cold storage. I also would have no idea how to contact who sent me the btc. I wouldn't want to send it back to the same address because it might be an address for an exchange where the btc would just get lost.

 In the first case, I would have received a previous transaction and be familiar with the sender so I would return the coins.
In the second case I would also be familiar with the sender and would refund the difference (maybe after subtracting the transaction fee in either case). Now, this could be problematic as the sending address could be from an exchange or a mining pool account and the coins would not actually be received by the sender.  I guess it would be prudent to try to contact the person before sending the coins back if possible.  Hopefully people would only send coins from wallets under their direct control.
 I could never keep something that wasn't intended for me.

 

Lol yeah maybe I would have done the same thing as you dude I mean maybe it was luck that is given unto God to you
so you receive bitcoin from god. and you should receive it dude.

If I receive a random bitcoin I will gladly return it. But the problem is to whom will i give it back. I will return it if the person who send me btc will show up and claim it from me by presenting datas tha he or she owns the btc. But at the end of the day I will not use that bitcoin until that person who owns that bitcoins shows up. It is not mine to its not for me thats my motto.

I would if he can prove that he is the owner of the bitcoins tht was mistakenly sent to me. I wouldn't just send it back to the address which was sent to me though. I mean I will wait for them to contact me and provide proof of ownership if they are telling the truth. If nothing came to take it bac then maybe I'll just keep it safe in the meantime and think over if I'll use it or not.

Yep, this is pretty true. I feel like what OP is really getting at is the same real life scenario of someone leaving some money on a table by accident and you find it, or a wallet - would you return it to its owner or go out of your way to find the owner.

 This is pretty weak justification for keeping something that isn't rightfully yours.  The coins have readily identifiable ownership linked to them - the sending address.  If you found a wallet on the street which contained money and identification, would you keep that because the person "obviously doesn't know" how to possess a wallet? 

I honestly would not give it back because its your own mistake and how can you even do this.
You always have to check your adress.