These are just samples; you may argue for one of these if you wish, but you aren't restricted to them. Another good place to look is in the list of reading response papers; they give a decent list of topics we've studied and suggestions about things you might want to argue about.
In this paper, I will argue that Hume is right to suppose that we don't encounter a 'self' within our experiences, but that this doesn't give us good grounds for rejecting the 'self's existence.
In this paper, I will argue that we do have a sort of identity similar to the sort of identity that plants have across time, and that Locke was right (and Hume wrong) to count as a genuine identity, not mere similarity.
In this paper, I will argue that Butler's objections against Locke's memory criterion of personal identity succeed, and that parfit's attempt to answer those objections via 'q'memory' fail.
In this paper, I will argue that Rahula and Parfit are wrong that losing a beleif in the self would help make us less afraid of death.
In this paper, I will argue that the person who enters to teletransporter dies, and ought to be afraid of his death.