There is a Walking Tree unique in Act 1, but I don't think they can be elites. However, there are also mobs such as Fanatics (the exploding guys in Act 3) who have a low possibility of spawning elite versions.
Diablo has several achievements The Takedown, Not So Tough Now, Champion's Collection, We Are the Champions, Keep It Rare, Rarin' to Go, A Rare Phenomenon, Trophy Hunting, Never Seen that Before, Special Snowflakes, and A Unique Collection for killing champion, rare, and unique enemies of each type - that should give you a complete list of which mobs can have elites, and by extension identify those not on the list that can't be boss/elite. As far as I know, there is no enemy which can only spawn as elite or boss versions but not both. Obviously, this is not true for uniques considering the tree encounter.
Some enemies that cannot be elite:
@yx.: Mallet Lords can be champions and rares as they're listed in the achievements, though they're one of the few that I haven't killed yet. I expect it's a combination of rarity of the mob itself and since everyone prefers to farm the other acts to avoid off-screen charges & easier to find NV stacks.