While playing Mercy, I tend to always keep everyone healed as much as possible, and try to never let anyone die. This is mainly due to habits I have developed from playing healers in other games where dying is bad. However, Mercy's ultimate can revive them within 10 seconds, so when should I let them die (i.e. stop healing them so I can revive them) in order to most effectively use my ultimate?
You should never let your teammates intentionally die just so you can use your ult revive. There's no point of doing this at all, and can only ever put your team further behind. However, if your team is about to be wiped out (say, by a junkrat ult), then you should usually get the heck out of dodge, then shift back in and rez everyone, rather than going down with the ship. In fact ditching teammates which are about to die is a good idea even if you don't have a rez. If it's just you and a Tracer guarding the point, and then 3 offensive heroes come in, then you're better of leaving the tracer to fend for herself and group up with the rest of your team.
So, when should you use your rez then? Well, that's simple! When it matters! Yes, not much of an answer but the idea is that there's no simple answer like "when you'll rez 3+ people". Sure, rezzing 3 people is normally going to be a good idea, but if you just wiped out the entire enemy team, most of the dead allies respawn timer is almost up, and you spawn is right next to the point then you're really just wasting that ult, because by the time the enemy team returns your teammates would have been back even if you didn't use your ult.
So, here's a few questions I'll normally ask myself when I have my Mercy Ult up, and folks are dead:
Which player(s) are dead, and what hero are they playing? If it's that Reinhart whose shield was keeping us alive then I'll happily use my rez to just bring him back, but if it's Symmetra, and her teleporter is already up, then I'd rather save it for when someone else dies.
How many players are dead? If you're going to rez 3 people then unless the entire enemy team is dead you should almost always use that rez.
How well is combat going? If the current battle is going really well for us, and we're going to wipe out the enemy team without me using my rez then I'll usually just save it, since chances are the team will be back before the enemy can pose a threat again anyways.
If I rez, are they likely to just die right away? If it's just you and a Tracer, and three enemies, then using that Ult is just extending the respawn timer on that Tracer. Your better off just letting her respawn naturally and get away from battle.
Does it look like more folks are going to die before the currently dead folks respawn? If there are two dead people, and I see that Junkrat is going to die before I can get to them and heal them then I'll wait a couple seconds so I can get that Junkrat in my ult too.
Are we in overtime? If we're in overtime then I set the bar a bit lower for when I'll use my rez, since it's better to use it and hope it makes a difference, then to keep saving it, only for the match to end with a loss.
How close are to capping the point, or did we just cap it? In either of these cases my bar for using my rez is lower, primarily because if we've got nearly a full team after capping the point then there's a good chance we'll be able to rush to the next point and and get it up to at least the first tick before the enemy team can regroup.
So this is a bit longer than I planned, and there's definitely the more I could list, but the letting your team die just to use your rez is a waste (but don't needlessly go down with the ship by healing a doomed ally), and learning the right time to use your rez comes with experience.
Never let someone die intentionally. TTK in Overwatch is low -- Heroes will be dying around you regardless, despite your best efforts.
On the other hand, as long as you're constantly healing your allies, you're generating a lot of Ultimate -- so a better question is not, "When should I let my teammates die", but "When should-- HEROES NEVER DIE!".
Personally, If you can land a rez for 2+ heroes, do it -- sitting on your Ultimate won't do anything, and saving it the entire match is the same as not using it. Whether you're on Attack or Defense, you should save it for a concerted push, where the sudden additional allies can swing the battle back in your favor (or secure an already overwhelming advantage as the other team tries to run back).
The answer is: when you are going to die from healing them while your ultimate is ready.
Considering that Mercy is the No. 1 target of the enemies' concentrated fire, you'll have to accept that you should be really, really passive when your ultimate is ready. Your ultimate is useless when you're killed off first, after all. There is even an in-game tip making this clear.
Instead, convey them that your ultimate is ready, and ask them kindly to make a bold push through the enemy defense (or a relentless defense against the enemy force, if you're defending). When there is a severe loss on the team, peek into the spot and use your ultimate. This will allow your team to be relentless while making a significant progress, unlike when going relentlessly without your ultimate.
Your ultimate is sort of the panic button, so you shouldn't be letting people die for the sole purpose of rezzing them. However, there are occasions to let an ally die. The first rule on this is that no support can save a player who is determined to get themselves killed - if the player sees that you're healing them, and charges into the rest of the enemy team, the correct choice is to let them die and focus on protecting or buffing someone else; the alternative is that you both die. Boosting things like Reaper's Ultimate can pay off, but this is rare and the best choice for achieving it entails using Guardian Angel to fly in while the ability is active or immediately before its use (do not attempt this without coordination).
The second case, which is related to the first, where you should let a player die is if trying to help them would get you killed. The support player is often the most important player on the team, and you should prioritize your survival. This is particularly true for flankers, who will take you to dangerous places if doing their job right but who also have the tools to get out alive.
The third case is triage - it is acceptable to let one player die to keep a more valuable member of the team alive; losing Tracer to keep Reinhardt is a fair trade, for example.
The fourth case is priorities - it may be more valuable to buff, say, Pharah's Ult than to heal someone else. This is massively context dependent, and requires tactical awareness outside your own role.