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On a special attacker, you want 0 Attack IVs to minimize confusion and Foul Play damage. On a Trick Room team, you generally want your Pokemon to have 0 Speed IVs. When are things like 0 HP, Defense, Special Attack, or Special Defense good to have?

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What format/rules are you playing with?
Why does it matter?
@X it matters because some sets like in the Battle Frontier would have moves like Wring Out, which is powerful if the target has more HP. However, in online battles, you're not really going to run into a Pokemon that knows Wring Out.
You'd probably want less SpAtk or Atk when you want to activate weakness policy (or frost breath on anger point) in doubles if that pokemon wouldn't use that stat otherwise.
@Porygon Oh, that makes sense. Let's just say Gen 8 OU then.

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Well, as Porgonzangoose was saying, if for some reason you know you are going to run into wring out, then minimum hp. You may want minimum sp def if you are running some crazy gaurd spilt strategy, as well as 0 def, so when you average those stats out and then they have less defenses. Much the same with sp atk, with power spilt. While all three of those are very uncommon and have a good chance to fail, it is possible to use 0 ivs for every stat and have a possible strategy come out of it.

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Oh and also there is the fact that if for some resonance you want focus sash to trigger (say a sash unburden hawlucha) you would want minimum of both defenses and hp.
Thanks!