Neat adds frames above Minecraft entities showing their names, health, and armor. Health bars shift from green to yellow to red as health drops, and only appear when mobs are unobstructed. A keybind toggles the bars, with plenty of configuration options.
Available for Forge and NeoForge for Minecraft 1.7.10 - 26.2, Neat runs entirely client-side.
Rent your own Minecraft server and add Neat with one click from the panel, then install it on your client to see those health bars.