DM Lair as always has a variety of great tips that always seemed to me like they worked well.

A random listing of stuff I've done that seemed like it worked well:

• Fighting on a boat versus creatures in the water that are trying to grapple players and drag them underwater
• Fighting in a place that has ranged attackers in a higher place shooting down on the players that aren't easy to get to
• Fighting against a human NPC that the players have to keep alive (e.g. they need information from him) but that seems to want to fight to the death
• Fighting a big bad that will leave if things start going badly for it, so players (after experiencing that the first time) have to strategize to come up with a game plan for how to kill it suddenly in order to actually win for real

Basically the place I would start is, what is the secondary goal besides "win the combat" that the players are trying to accomplish? E.g. in the above list it would be "rescue the other player who got dragged in the water", "get somewhere else before we get killed by all these arrows", "judge how close this guy is to dying so we can start using non-lethal strikes at that point to keep him alive", "plan out the all-out attack at the end, then judge the right moment to execute it." Generally that'll make for a lot more dynamic combat and let the players feel like they gave some needed decision-making input to the process aside from just "lore and motivation, hit hit hit heal hit hit, done".

It can help if you think in terms of intense fight scene tropes from movies and TV that you like. Especially if the goal of an encounter is very clearly not to kill the enemy.

I once ran a combat against a dragon on a rickety rope bridge over a huge canyon. That was an exciting fight, and the party never considered that they were actually going to kill the dragon then and there.

My prep for that session was essentially deciding what the rules were for the rope. I decided it had a certain amount of "structure points" and then made a list of things that would reduce its structure points (eg. The heaviest character in the party steps onto the bridge, two characters end their turn on the bridge at the same time, a character dashes on the bridge, etc.). The bridge was just over 60ft long, so it was just barely possible for one character to cross it in one round.

Then, I came up with rules for the dragon. The players knew there was an adult white dragon living in the mountain on the far side of the bridge, and they were on a quest to slay it.

The first round just involved them trying to cross the bridge with no distractions. At the end of the first round I tell them they hear a roar coming from the mountain with the dragon.

Second round. The dragon is in the sky, but it's going to take another round or so to get to the canyon.

Third round. One PC is across and another is halfway out. The ropes are clearly starting to strain and fray. The dragon is here. It's not trying to kill them with claw/breath attacks though. Its goal is to stun them with its frightening presence and then swoop down, grab them and carry them back to its lair. It grabs the Sorcerer who is on the bridge and dangles him over the canyon.

Fourth round. The Barbarian runs out onto the bridge to try and wrestle the Sorcerer away from the dragon. The Sorcerer triggers a wild magic surge and transforms into a potted plant, thus causing the dragon to lose its grip and drop him. The Barbarian is able to use a reaction to reach out and grab the potted plant before it falls hundreds of feet into the canyon. The dragon roars and attempts to frighten the Barbarian but it fails.

Fifth Round. The Barbarian flees to the safety of the far side. As he does so though, he dashes and thus exhausts the last structure point on the bridge. The bridge snaps and the Barb has to grab onto the falling bridge and swing down to be left dangling from the bridge. Potted Sorcerer plant in one hand and the other gripping the dangling bridge. The NPC who was travelling with the party, now trapped on the wrong side of the canyon, tries to harass the dragon just enough to give the Barbarian a chance to climb up and escape. The Sorcerer reverts into a person and climbs up the dangling bridge.

Sixth round. The PCs are able to all get to the safety of the far side of the chasm. They are separated from their NPC companion, but they can hide from the dragon in a narrow tunnel in the rock face.