From Proceedings of the Symposium on Oxygen Electrochemistry and Water Research 2002, 36 (1), 85-94:
$$
\begin{array}{lcc}
\text{Formation}&:&~\ce{2H+ + O2 + 2e- &->& H2O2} &\quad E^0=\pu{0.440V} \text{ vs. SCE}\\
\text{Reduction}&:& ~\ce{H2O2 + 2H+ + 2e- &->& 2H2O} &\quad E^0=\pu{1.534V} \text{ vs. SCE}\\
\text{Direct water}&:& ~\ce{2H+ + 1/2O2 + 2e- &->& H2O}\\
\text{Decomposition}&:& ~\ce{H2O2 &->& H2O + 1/2 O2}
\end{array}$$
($\text{SCE}$ stands for Saturated Calomel Electrode)
Another strange suggested reaction involves the anion $\ce{HO2-}$ (Abel E.: Über die Selbstzersetzung von Wasserstoffsuperoxyd. Monatshefte für Chemie 1952 83(2) 422–39.):
$$\text{Decomposition 2}:\ce{H2O2 + H2O- -> H2O + O2 + OH-}$$
At the cathode occur at the same time the hydrogen gas evolution:
$$\ce{2H+ + 2e- -> H2~} \qquad\qquad\phantom{00} E^0=\pu{0.242 V} \text{ vs. SCE}$$
Meanwhile, at the anode, oxygen gas is evolved:
$$~\ce{2H2O -> 4H+ + O2 + 4e-} \quad E^0=\pu{0.987V} \text{ vs. SCE}$$