Lancer is really good about that, to the point where "Mission Objectives" are built into the encounter design section. While the appeal of "mission objectives" varies from group to group, in my experience, the vast majority of "average" players enjoy them.
Some groups I've played in are even of the opinion that any combat without an objective is a waste of time. In their opinion, an encounter that consists of a hungry monster trying to eat the party is meaningless filler that's wasting everyone's time. Especially in more modern systems where healing is free and relatively quick.
I'm not quite that extreme, but I think that extreme opinion can point at some useful advice. When GMing, you should consider the purpose of every combat encounter. It's fine if the purpose is something simple like to establish that the Forest of Nightmares is a dangerous place, but it shouldn't be just because you have to keep your players entertained for 5 hours.
In my experience, two
very different groups tend to dislike objective-heavy combat; that's what I meant above about "average" players enjoying them. Players who invest heavily into character builds can be upset that their build doesn't get to do the things it was designed for. If half of your turns are spent running away or throwing a mcguffin, you'll have less time to use that sweet combination of feats you found. Most players don't treat their character build like a trading card game deck though, and enjoy the variety.
On the opposite side of the spectrum, the real creative, narrative types can get frustrated as well. The kinds of people who swear that if you don't like FATE, it's because you're doing it wrong. To them, if a scene is about breaking an npc out of prison, for example, why are we adding things like tactical movement and action economy by framing it as a combat? I want to do something cool like bounce the mcguffin off the wall so I can swing a rope across a chasm and catch the mcguffin on the other side. But because we're breaking my turn into discrete actions, I can't do that. Again though, most players like combat, so this isn't an issue.
Sorry for the long post, but mission objectives are something I do a lot, so I also want to list a few of the objectives that have worked well for me.
- Capture the flag: The players need to retrieve some item, and bring it back to some safe zone or extraction point. One time, I added a similar objective for the enemies, so a few players had to play defense, just like real ctf. It was fun in the moment, but I think it just adds too much overall.
- Puzzles: Occasionally I used to throw old-fashioned block puzzles or tile puzzles at the players. They weren't super engaging until I added combat elements simultaneous to the puzzles. A boss whose AC drops when blocks are pushed to the right position, or an enemy spawner that only turns off when colored gems are matched to their matching pillars. These have been some of my most memorable combats.
- Escort Missions: This only works if you have an npc the party actually likes. If you do though, adding enemies who don't care about the party and only want to kill/kidnap this npc leads to fun combats.
- Assassination: Like an escort mission in reverse, the party needs to kill/kidnap one specific target, and doesn't care about the mooks except in so far as they're blocking the way to the target. Sometimes the party needs to kill someone and leave before being overwhelmed, but a "Command Ship" fight, where all enemies stop fighting once the target is killed is fun too.
- Multi-Team: aco175 mentioned something similar, but if you have two or more distinct groups of enemies, the players will feel really smart if they get one group to attack the other.
- Auto-scroller: A hazard (spreading fire, collapsing building, poison gas cloud, etc) spreads across the battlefield, and the party needs to avoid this hazard while fighting off enemies. Whether or not the enemies are immune to this hazard can change up the feel of the fight a lot.
- Bridge/Gate guard: Not sure if this really counts, but a lot of fights in rpgs boil down to "we want to get to <place> but the enemy doesn't want us to." In fights like these, the party could easily disengage and run away once on the other side. This only feels like a victory though if it's clear that killing every enemy is unfeasible, like if reinforcements are endless or something.
