I was taught to balance redox equations with acid/base considerations. Instead of arbitrarily adding $\ce{H^+}$ and $\ce{HO^-}$ ions and memorizing separate rules for acidic and basic solutions, I was taught simply to keep these four things in mind:
1) Charge must be conserved.
2) Mass is similarly conserved.
3) Do what's thermodynamically more favorable. For example, in strongly basic solution, $\ce{O^2-}$ oxygen ions come from not hydronium ion (because that doesn't exist in significant quantity in basic solution) and not from water (because that requires heterolytic clevage of 2 $\ce{H-O}$ bonds but instead $\ce{HO^-}$ because that only requires clevage of only one $\ce{H-O}$ bond.
4) Strongest base reacts with strongest acid.
On the other hand, here's a gem from Chem Wiki by UC Davis:
My question is:
1) How come I've never seen my professor's method mentioned anywhere? I've Googled, looked at scholarly papers; looked in advanced analytical textbooks, etc.
2) How were you taught?
3) Which way do you think is more advantageous?