I going to look at this in a couple of ways, units I hate to lose and/or units I love seeing my opponents lose or units that are targetted by your opponent.
Germany:
The Bomber. Bombers are deadly, not only for the 4 attack but for the range and threat level they provide. I tend to play it a bit safe with mine, but can’t tell you how much of a relief it is (as an Allied player) to see the Ger Bom go down to AA-fire in rds 1-3.
The Fleet. Sunk on UK 1, but if anything escapes to G2, consider it a bonus.
Russia:
No VIUs. Exception would be if they bought any air, but there is no specific unit that they start with. They mostly play with basic units of Inf/Rt/Arm.
Japan:
NO VIUs. They typically make enough where any unit can be replaced.
UK:
The Bomber. Same rationale as the Ger bom, the range and threats it can provide is unmatched, but unlike Germany after rd 1 or 2 it becomes hard to replace. The exception to not risking the bomber would be if you can use it to help take out the Italian Fleet in rds 1-2.
Sz 2 BB. If it survived G1 added with an AC and a couple fodder ships you pretty much have an unsinkable fleet at the end of UK1 and can concentrate on trns and getting troops to Europe. It just helps with the Atlantic logistics if you have a heavy hitter already on the board.
Egy units. If you have any of these at the start of UK 1 your job just got a bit easier.
2 Aus units + trn. You can create some interesting moves/counters with the threat of landing these 2 units in multiple places early in the game.
Italy:
Their Fleet. Should be obvious, but without it Afr is a lost cause. It should also be the #1 target of the Allies in rds 1-3. If it is sunk early the Axis can be in a world of hurt.
China:
The Ftr. You should never get to use it.
US:
Bombers. (see Ger/UK).
Pearl BB and DD/trn in Sz 56. You should never get to use them. If any survive to US 1 its a huge bonus.
Sz 44 fleet. Only b/c of the AC, either it starts the the core of your Pac defense or it gives you a massive projection of power in the Atlantic in helping you secure Sz 12 in rd 3 while the UK can shift to Sz 6.