In most real estate transactions, the appraisal is ordered by the lender. While the home buyer pays for the report as part of the closing costs, the lender retains the right to use the report or any information contained within. The home buyer is entitled to a copy of the report - it's usually included with all of the other closing documents - but is not entitled to use the report for any other purpose without permission from the lender.
The exception to this rule is when a home owner engages an appraiser directly. In these cases, the appraiser may stipulate how the appraisal can be used; for PMI removal, or estate planning or tax challenges, for example. If not stipulated otherwise, the home owner can use the appraisal for any purpose.