I'm not too fond of the trend towards regenerating health in FPS/TPS games. This said, two or three games come to mind which had reasonable compromises:

• Halo - shields regenerated, sure, but if you wanted to recover health, you had to find a medpack;
• Resistance: Fall of Man - limited regeneration (round up to the nearest quarter);
• Kill.Switch - somewhat similar to how one of the Marvel/Capcom crossover games (the specific title escapes me at present) let tagged-out partners heal. Hard to describe; just look up dial187's playthrough on YouTube.

Speaking of being able to stock up medical packs: this is not necessarily a bad thing - just look at Dead Space and Duke Nukem 3D.