Well, since I enjoy running lower level quests for favor and such, and it is difficult to find people who want to do these the way I like to do them (Ie: even on a favor quest, you kill everything, smash every barrel, find every secret possible, etc...none of this "rush to the end and ignore everything else" nonsense"), I end up soloing quite a few of them. This has run me into the issue of some of Turbine's design mechanics, which make certain quests absolutely positively impossible for 1 person to accomplish alone. I think a list of such quests is in order.
For the purposes of this list, there is only 1 qualification that matters, and that is a lever, switch, floor pedastal, etc that requires one person in one location, and a second (or more) person in another. So for example, the difficulty of killing Velah by yourself does not qualify VoN6 for this list.
There are 2 types of quests that need multiple people. There are ones that require floor runes to be stood upon, and there are ones that have levers or switches, or wall runes, or...whatever, that need to be activated. Floor runes are essentially pressure-activated, and any creature standing on them is sufficient. With clever use of spells like Summon Monster, Halt Undead, Hold Monster, etc, you can "convince" NPCs to stand on the floor runes and substitute for a player. Switches, wall runes, levers must be activated by players.
Floor runes:
The Xorian Cipher, House J. Requires 4.
The Tomb Of The Burning Heart, House P (Necropolis). Requires 4.
Levers/Switches/Runes:
Rest For The Restless, House P. Requires 2. [Can be solo'd if you are willing to recall out and enter]
The Missing Party (Delera's 2), House J. Requires 2.
The Tomb Of The Shadow King, House P (Necropolis). Requires 2.
The Vault Of Night (VoN5), House K. Requires 3.