With very few exceptions, the T1 uniques are the "insanely strong uniques that you would create an entire character built around" category of items.
The only T1 unique I own is "Pledge of Hands", for example. Mine is a 5-link. Pledge of Hands gives 100% increased mana, something around 150% increased spell damage, and supports spells socketed into it with LEVEL 30 spell echo (normal max level spell echo is 20). Therefore I effectively am using a better-than-normally-possible 6-link spell, plus the massive mana bonus is enough that I can reserve 92% of my mana *and* regen enough mana to spamcast Arc, my spell of choice. It's CRAZY strong, I got a steal for it when I bought it for 9 exalts (average at the time was ~10 exalts for a 4L or below, ~13+ exalts for a 5L, and like 40+ exalts for 6L).
Shavronne's Wrappings has a bunch of energy shield, plus the mod "chaos damage cannot bypass energy shield", which enables "low life" builds (which take the keystone "pain attunement" to do tons of damage, along with running an abnormally high amount of auras, and have lots of energy shield).
Mjollnir has a chance (30% for the non-legacy version) on every weapon hit to cast any lightning spells socketed in the weapon. This results in psychotic damage, because the weapon itself does decent damage, you can use a 6L attack setup, *and* you trigger 2-3 spells nonstop. It's also just a joy to explode screens with insane amounts of spell effects triggered by Mjollnir.
There's other T1 uniques but Shavs/Mjoll are by far the most sought-after.
Some day I'd like to own them all - T1 uniques enable you to do VERY cool things.
