Yes, if you play as a Redguard or Imperial, your health auto-regens.
Major Edit:
Correction, but still yes,, only if you choose the proper birth-sign (like Lord), sorry for the mis-info
Sorry, health never regenerates in TES IV: Oblivion (without mods). The Lord has a less power to heal, it still does not regen health automatically.
I've also noticed that you don't automatically harvest everything. I assume thats a skill perk that you get better at harvesting the ingredients in the world as you level up? If so, i kinda dig that...
I've noticed several things like that. In Oblivion there is a percent chance of successful harvest. And that depends on the plant. Some plants like Flax are easy to harvest, some like many mushrooms are more difficult. It's not related to a skill perk.
There are lots of things like that in Oblivon. Armor degrading of course. Haveing to find higher level alchemy equipment too.
And even more things like that in Morrowind. Like spells and potions have a chance of failing.
I guess these things are reduced due to "streamlining"
There really is no comparison , Skyrim is far superior to Oblivion.
That is of course a matter of opinion.