Miners Choosing Transactions

[Bitcoin Betting Guide]

Is it right that miner can choose weather or not to include valid transactions in a block? I have heard it mentioned that they can but it seems problematic to me as it means they can black list addresses or be not neutral. If a valid transaction is waiting to be confirmed when they find a block they should HAVE to confirm it, that is what they are getting the block reward for doing.

[BlockChainLottery]

Yes.
But the Bitcoin documentation is giving directions (implemented in version 0.8.2) of how to include transactions in a block.
https://en.bitcoin.it/wiki/Transaction_fees#Including_in_Blocks
I think most of the miners will stick to this, and minimizes the chance that somebody is blacklisted and cannot make any payments ever. It does not mean that individual miners cannot choose how to include transactions. They can even choose to mine only empty blocks, which is more resource efficient from the perspective of the miner. But the other miners must also check and agree with the found block, thus it's not entirely up to the one who mined it. I think this gives enough counterweight to balance this problem. The 'HAVE' you are talking about is just not possible, because everyone can code its own miner.
A decentralized system can give you a headache sometimes.

[oxfardk]

absolutely it's right the miners can decide promptly to discard transactions

[cp1]

Theoretically they don't need to include any transactions.  But then they wouldn't get to spend the coins that they produce.  And if they started pulling crazy stuff with which transactions they included then the price would fall and the coins they produced wouldn't be worth anything.