The in your face answer to this is to of course pay down expensive high-interest debt first, credit cards and personal loans spring to mind. These can sit racking up 20%+ interest, a rate of return you will be hard-pressed to beat through investing. Therefore it makes sense to get rid of these as fast as possible.
This will probably be the only time I wholly endorse sinking yourself into more debt. But this is the best debt you could possibly ask for. Interest-free money! I wish I would have thought of this earlier on. In my second year at university it hit me, why wasn't I taking everything I could from my student loan. I had a part-time job which covered the majority of my expenses and in an effort to remain as debt free as possible was drawing only a small amount of my living costs per week. Oh, the missed gains.