Or to be more exact, what are the cards (from any sphere) that you would never wish to leave out when it came to constructing a single deck for solo play?

(I know that there are many people now who prefer to play two-handed, but for this thread I was rather hoping to focus solely on single decks)

I would say it depends what spheres/heroes you are running. So I would break the question down by sphere:

Spirit - A Test of Will above all

Leadership - Steward of Gondor (unless excluded by theme - I've been playing strict theme myself recently), Sneak Attack

Lore - Daeron's Runes

Tactics - Feint

Gandalf - I don't think there's any deck that he doesn't strengthen.

There are certainly others that could be added, this is just a very brief starter

Thanks for your reply, jjeagle.

You're right of course, heroes will often impact upon the cards a player feels that they need to take.

Furthermore I agree with all of the cards you have listed.

In regards to Steward of Gondor, I always used to have difficulty including that card in any deck that wasn't Gondor or Rohan themed. I eventually got around it by imagining that Gandalf or some other powerful individual in Middle-Earth was convincing Denethor to aid the hero with a portion of Gondor's vast resources.

Spirit Glorfindel is ridiculously good along with Light of Valinor and they may have made those cards specifically for solo because it was so difficult earlier on in the game.

Readying effects are super important for solo for me because you don't have another player to step in and save you if you need it so: Unexpected Courage, Miruvor, Tactics Boromir (paired with Lore Aragorn is great for abusing Boromir's ability).

Having one hero for each questing, defending and attacking is also important to take care of the key aspects of the game so: Eowyn, Beregond, Legolas but flexibility can also be good: Gimli, Glorfindel, Elrond, Aragorn.

Key cards that are in all decks have already been mentioned above but also scrying is great for one player because you can potentially know what will always come off the encounter deck: Denethor, Henamarth Riversong, Rumour from the Earth, Risk Some Light

Those are a bunch that I like!

I have most experience playing spirit solo and also think it is the most effective sphere to play solo with. I think any deck that starts with:

Heroes: Spirit Glorfindel + Eowyn + some other hero

Cards:

3 x A Test of Will

3 x Light of Valinor

3 x Elrond's Counsel

3 x Gandalf (Core)

2 or 3 x Arwen Undomiel

Is already a very strong basis for a solo deck. You can then splash another hero and other cards depending on the quest. I always try to get Light of Valinor in my starting hand to start with 7 questing power from Eowyn and Glorfindel, with Glorfindel ready to contribute 3 attack on the same turn. Surprisingly, I don't consider Unexpected Courage a must-include, depending on your third hero, because Glorfindel and Eowyn don't actually benefit that much from it.

I actually think Glorfindel + Light of Valinor is overpowered, and am trying to move away from using it. However, a mono-spirit deck based on Glorfindel, Eowyn, and Dunhere would be my go-to deck for tackling most quests, especially those that don't involve combat-oriented victory conditions.