The speed at which a monster regenerates its life depends on various things. Most crucially is the difficulty of the game you are playing in. Another factor is their HP total; the regeneration is a percent of their maximum life - in other words, the more life a monster possesses, the more it heals each second.
Monster Heal is something not many players may know about in Diablo I. The only ways to really notice that such a thing exists is through one of Pepin's randomized gossip lines, or extensive use of Golem. And even then, it is generally not too big of a hindrance (or an aid, in Golem's case), because within the time such regeneration would be useful, the monster is simply overwhelmed by the player's damage.
Unfortunately, for those few who do not have enough of an edge, Prevents Monster Heal is not available in the first game, even with Hellfire installed. Equip your hero with that in mind.
Diablo II/Lord of DestructionEdit
In Diablo II and Lord of Destruction, Monster Heal is much more of a boon to the minions of Hell (or to you, if it's your Hireling or Summons), because while they did not regenerate while the hero was in town in the original Diablo, they will in Diablo II as well as the expansion. Another factor to that regeneration is the actual monster type; that is to say, a Minion of Destruction in Nightmare Difficulty may regenerate faster than a Steel Scarab in Hell Difficulty.
There are a couple ways to counter monster regeneration, however. Unlike the original Diablo, "Prevents Monster Heal" does exist, in an easily obtainable affix for both Magic and Rare Melee Weapons. Alternatively, the regeneration can be counteracted with the damage over time effects of poison or the even better Open Wounds that does bleeding damage over 8 seconds and scales with your hero's level, usually inflicting more than enough to prevent the monsters' regeneration.
Although Monster Heal is no longer around in Diablo III, before a patch, if the Nephalem fell in battle against a Rare, Champion or Unique, that monster group could heal itself to full. This frustrated too many players however, resulting in Monster Heal being removed.
The only other way a monster can heal is the Vampiric affix, and even that affix can only happen on legacy Elites.
Bosses will heal to full if they defeat players though, forcing them to begin the fight from scratch.
Innate monster abilities may allow them to renew in battle: Morlu (of either type) may partially heal if they are brought near death (into their ash state), but not killed quickly afterwards.