The entire Lockpicking tree. Even when playing a Theif I never touch it, same goes for modded as well. Once you know how to lockpick, even Master level locks at novice lockpicking levels are pretty damn easy... not to mention lockpicks being plentiful, as money is easy to obtain. In the end I modded the game so you can smash open locks with a 2-hander, or melt them open with magic, though you can only bust open certain locks depending on your skill level in destruction/2-handed.
Speech is another one, though the only reason I ever put points into it was to unlock the rare Alchemy ingredients from vendors. Asides from that, it ended up the same as lockpicking for me. Modded however, It became a must have if playing as the Dragonborn, since shouts are powered up by the speech tree <3 *seriously, why the hell did they not do this in the vanilla game =_=*
With Enchanting and Smithing being in the game I never touched the armour perk trees as well. Pretty much all the armour perks are made redundant with the crafting trees, and with player skill. Once again, mods balance all of this, making those trees needed if using armour.
In the end it all comes down to roleplaying ect. Before I played the PC version I had the min-maxing mind set, so pretty much 75% of the perks in the game were unused, with just over half of them being useless or redundant due to player skill, or spells/enchantments/whatever already added by the game… or bugs/glitches.