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Different artifacts are good for different individual games.
But naturally, resource-giving artifacts are always useful.
Besides that, Boots of Speed are always handy, along with a couple of Gloves of the Horseman (put them on at night, and in the morning you're full of strength and energy to cover almost twice the distance :-)), Angel Wings, and the Speaker's Hat for Dimension Door.
Otherwise, everything else depends on the situation.
If it's the start of the game, for example, but you've already managed to get Earth Magic - it's very good to snag a Tome of Earth Magic for Town Portal; if your hero has many shooters, the Golden Bow will be an invaluable gift; for a Barbarian, artifacts that block magic and increase creature speed; for Necromancers, ones that boost Necromancy skills (by the way, I wouldn't say the Cloak of the Undead King is as cheesy as many claim - a lot depends on the map, but if the map has many neutrals, then of course it will be sad for the opponents :-)), and so on.
And in general, I really like Boots of Speed and Shackles of War (I don't like it when some scumbag with a weak army, but a strong mage, first tears me apart and then successfully escapes with all the artifacts, the parasite :-))