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Blessed seven league boots drastically increase your movement speed both in dungeons and the wilderness. They are widely considered to be the best boots in ADOM. Only wish for them if you don't already have a pair.
As of version 1.2.0, it is only possible to get one pair per wish
A ring of weakness is typically useless to the extreme. However, with proper planning, it is possible to raise all stats to 99 with one. See its page for details.
Don't wish for this if you don't want to scum massively. In 1.2.0, the scummy features of this item no longer work, and it should not be wished for.
The Archery skill increases missile damage, and can be quite useful to anyone attempting to use missile weapons
Archery increases to-hit and to-damage boni by 4 and 2 respectively at skill level 100; more important advantages include access to the Lightning Shot (missile attacks have energy cost reduced by 10%, cumulative with other modifiers) and Eagle Eye (+3 to-hit and to-damage on missile attacks) talents.
For PCs with low toughness such as any mist elf, wishing for these may result in an effective increase in To of 8: first potion increases To by 2 and sets To potential at +2 value; then To is trained for 2 points; then the same process is repeated for the second potion. Only two can be gained per wish. Blessing the potions before drinking is a must.
Eternium tower shields are the best non-artifact shields in the game. They are very good defensive items, especially in the early-mid game.
A single wish will grant 2-4 shields potentially allowing higher than base stats. Note that as of 1.2.0 you 1. can't cast spells, 2. receive a significant ranged to-hit penalty while dual-wielding shields.
Regeneration is a powerful intrinsic that allows the PC to recover 1 HP per turn per regenerating item.
This is a significant enhancement over most conventional sources of healing available in the early game, and can go a long way toward keeping a weak PC alive (especially for mist elven PCs). Most of these items are fairly rare and have high danger levels and are thus difficult to acquire prior to the Casino. Among these items, rings are typically a better choice as two of them can be equipped simultaneously and are highly resistant to damage if protected by gauntlets.
Rings of ice protect worn equipment from fire damage, very important in the Tower of Eternal Flames. They are relatively less important in other areas of the game, and not worth a wish. Note that as of 1.2.0 neutral PCs may receive the ring from the dwarven mystic.
Fireproof blankets protect your inventory from fire damage, which is always useful. They can be useful when attempting the Tower of Eternal Flames, but their wish-worthiness is debatable.
A wish for the emperor moloch will grant ~30 greater molochs, assuming the emperor has not already been slain. These can be killed for a LOT of XP, if the right tactic is used.
A banshee can clear the bug temple relatively safely, if the right precautions are taken (see here). The rewards include three scrolls of corruption removal, a pile of 12 quarrels of slaying, 6 potions of ultra healing and a paddedelven chain mailof resilience (great for Monks), among others.
This is a VERY dangerous wish to the unprepared. As of Version 60, this tactic no longer works. The banshee appears and disappears, with the Genie offering you another wish.
Speed is useful always, essential rarely. Use with discretion. VERY helpful when fighting Andor Drakon; this is typically the only time you will wish for speed. This boost is mostly temporary. Only a small permanent increase will remain.