Can you take your IRA account and transfer that IRA account into another individuals IRA account?

No, you can not transfer an IRA account from one person to another. IRA accounts are only for one particular individual. You would have to take a distribution from your IRA account and deal with any tax consequences, then give that money to the other individual so that they could contribute it to their IRA account. They would have to abide by the limitations placed on contribution limits i.e. $5,000 per year (as of 2009) for individuals under the age of 50 and $6,000 (called a catch up contribution) for those over the age of 50.