Winging this, not sure on order exactly. The order of 1-5 is subject to change and I probably will miss an obvious item along the way, as I do this off the top of my head real quick.
1. Enigma - Pretty self explanatory. Not only can any char Teleport now, this item is actually extremely good in a Sorceress slot, if rich enough to meet all of your other Chars that can't teleport. Nobody typically uses it there, due to not getting full potential of free teleport. But it still kills in that slot, that is how good it is. Skills, ability to back off on tons of strength, lots of MF, DR%, adds some life and +14 to life after each kill. That adds up nicely for characters like a Javazozn. This and BotD was what everyone wanted when 1.10 came out and Enigma has certinaly been the one to hold up.
2. Grief - I sometimes wonder if Grief was meant for just Smiters, which is where it got its name first for being big. Everyone was going for BotD, Doom, Beast or Death, because they looked real pretty with high end ED and a list of other mods. The real gem was Grief and being that it had +XXX Damage, as opposed to a juicy looking looking %, people initially went for the high ED runewords coming out of 1.09. Or maybe the people at Blizzard were trying to low play it as a Smiter weapon, while using Grief and hoping it would take time for people to understand the +Damage mod was tops and hoping they could use Grief as their weapons, while everyone was chasing expensive BotD's, etc..hahaha.
3. Eth Reaper's Toll - This is personally my favorite Mercenary weapon by light years, unless it is a pure lightning buildd(or possibly a few other elemental builds that an Infinity can really make stronger). For any melee character, it is basically the equivalent of the Grief except for your Merc. The CtC Decrep means you'll rarely be dealing with a Physical Immune ever and get a huge damage boost constanty, The damage that is made even stronger by being ethereal is great, the built in, high life leach means you can focus on hitting your IAS BPs, resists and other important things. It just turns any good melee character into a great one and is still vary viable to use on non-melee builds, if you don't need a certain aura from a weapon.
4. Infinity - Obviously this all comes down to having Conviction Aura. Some of the most lethal builds are over the top because of this item. Javazons, Trapsins and Lightning Sorc(personally not a huge fan of Lit Sorc for PvM lol) really sticking out. I assume Tesladins can utilize this as well? Just what it does for the three original characters I mentioned, makes it an absurdly powerful thing to have on a Merc of one of those characters. The huge -LR% always confused me, since it only works for the Merc itself I believe. I don't know if that was intentional or not, as it seemed like just a big tease for people when it was released. Blizzard doesn't like to walk back anything, so if they messed up somehow, I guess it will always stand as a trick. If it it did work for character's damage, it probably would be a bit overkill. Maybe somebody knows more than I do about that and can inform me, as a Merc with Infinity doesn't exactly slay monsters too fast or have a reason to be stacked with lightning damage. Still, wonderful item.
5. Insight - This isn't the strongest weapon in slot for any finished character and probably isn't the best weapon in slot for any finished Merc, outside of a few mana intensive builds. What I find so great about this item is: 1. It is absurdly cheap to make. Finding the 4 os weapon is the hardest part. 2. It can be used very early on in the game 3. The Meditation Aura means that you can basically spam any spell you want and never have to worry about mana potions or running out of mana. This item may not be overwhelming, but anyone playing an untwinked playthrough is going to be trying to make one of these for their Mercs as fast as they possibly can. Some high level characters I still use Insight on because of the mana assistance. Plus this item has pretty damn good damage, especially for early on in the game if you can find a good base. An Eth lvl 25 base can put you in a position where you Merc can output bigtime damage for a long time. This item gets on my list mainly for how easy it is to obtain, how early you can utilize it and because it adds some amazing attributes on top of that.
Honorable Mention: SHAKO. Shako goes good on every character. Some may have a better Helm option, but you might not find your CoA, Griffon's, Runes for RW and end up using a Shako. But Shako still rocks. +2 Skills, lots of life+mana, 50% MF, 10% DR and don't forget the most extreme +2 to all attributes. You can PTopaz it for a MF Helm that offers great mods, or Ist it and look like a true baller. You can Ber it and help assist with hitting high DR%. Or you can do the greatest thing ever and 'CHAM' it and never have to wear a Raven Frost on a non-melee build again. I've never found a Cham in almost 20 years of this damn game, so I can only relate to my B.Net experiences of CHAMing things and this is about SP.
Also think Fortitude deserves some type of Mention. It is not necessary, but it sure beats out the old school 160/60 that most good melee characters would use through 1.09.
Cheers to all of the items I missed out on and will probably realize deserves a higher slot than one of these!
*Disclaimer: I just woke up middle of night/early morning and wrote this up in a stage of fog and haze, because I thought it looked cool. I may have a completely different opinion when I wake up in the morning forrealz. After rereading my posts, I realized the Merc got quite the upgrade after 1.10/1.11.