HPLC is used in a a very wide range of tests in hospitals: I could type here all day long and not cover half of them. All the same, as a start how about:
Sickle cell screening
Identification and separation of metal binding proteins in human tissues
Distinguishing forms of haemoglobin in the circulation
Drug plasma level analysis
Monitoring by blood by-products during drug trials
Detection of heavy-metals in plasma from A+ E blood samples
Cellular phosphatase analysis in oncology
Preparatory steps in Edman Sequencing
Drug stability testing in shelf-life analysis to confirm manufacturers data.
HPLC equipment can vary considerably in sophistication. At the university where I work, I understand we have one of the most expensive and sophisticated models in the UK in the Chemistry Department . The problem is that due to budgetary constraints, UK hospital trusts often cannot afford the most advanced equipment. So at the end of the day, the equipment is only used to the limit of its capability in each hospital.
We've had two new HPLC state-of-the-art machines installed in my biochemistry department last month but in general, universities with medical schools and world-famous teaching hospitals are usually the better equipped.