There is only one artifact that provides NO bonuses: it is needed to complete mission 1 of campaign 4; this is the "Ring of the Shadow-Marked."
All other artifacts have at least some bonuses.
The three most useful artifacts (in my opinion) are the unicorn horn bow, the boots of levitation, and the angel wings (the last two are story-related and are only given in two campaign missions: the boots in mission 4 of campaign 1, and the wings in mission 5 of campaign 3; the bow can be obtained in any mission where there is an artifact shop, or where they are present in the script).