Apparently all ordinary enemies respawn, but so far I haven't encountered a boss that respawns, mini-bosses included.
Dark Souls – Do Bosses Respawn?
dark-souls
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Best Answer
In conjunction with zero298's answer, a "boss" enemy is any enemy that has a static, on-screen health bar. These bosses will only spawn once per new game. Only entering a new game+ will allow them to respawn. However, if you wish to face them again before entering ng+, you can use the White Sign Soapstone and assist other players in defeating them.
These enemies are: (in general order of encounter)
Area Bosses: Once these bosses are defeated, you cannot summon/be invaded in this area anymore.
Optional Bosses: defeating these do not affect summoning/invasions (with the exception of the Undead Asylum; since you have already defeated the area boss before invasions/summoning became available). This means if you wish to summon help for these fights, you will need to do so before fighting the main boss.
DLC Bosses:
There are also a series of enemies throughout the game that are not really considered "bosses" (sometimes referred to as "mini-bosses"), that will only spawn once per new game: