For example: "Have another monster/group enter the fray halfway through the battle!"
That's good once. Exactly once. Do it a second time, and your players will never again assume that the monsters they see when initiative is rolled (if you use initiative, see below) are all there is to the fight. Just like how if the DM makes use of explosive runes during session one, no PC will ever read any writing during that campaign ever again. Not that I'm bitter, or anything...
So without further to do, here are my tips for making D&D (etc. etc.) combat more fun.
- Get rid of Opportunity Attacks. There are many reasons for doing this. But the most important is that OAs penalize PCs for moving. Moving makes combat interesting. OAs = no movement = boring combat. You learned to put difficult and fancy terrain in your combats from some other list? Great! Now watch the PCs not use it at all for fear of getting hit with a sword on the way there...
- Make initiative better. Look, in-line initiative is the easiest way to arbitrate combat for beginners, but after a few years of experience, it becomes a hinderance. When everyone knows they are free for 5 minutes or more after their turn is done, people start leaving the table for beer and chips and phone calls and Starcraft II, etc. Don't let that happen. Your initiative system (or your ability to narrate and move combat without initiative at all) needs to keep everyone glued to their seats. I think popcorn initiative may be the best middle ground. If you reeeeeaaaaally love in-line initiative, allow combatants to knock other people down the order with stunning effects, etc. Keep the order dynamic.
- A miss should only be "plain ol' miss" about a third of the time. There is a whole world between fumbles and hits that few DMs and players every explore. I have my own fumble rules, but when it comes to interpreting a miss, I like to fly by the seat of my pants. For example, your longsword-wielding paladin player has just rolled a 2 against his dark knight nemesis. Are you just gonna let this be another miss? No! What if that dark knight caught the paly's sword blade between his armor and shield? Cool. And a free pseudo-grapple by the opponent isn't so harsh as to be fumble territory. Just let PCs do this to enemies too.
- Escape plans. Any moderately intelligent enemy should have one. If they are hurt or outnumbered, they flee. And this is a win-win, because either they can become a reoccurring villain if they get away, or it starts a chase (which your combat should have more of too).
- Don't roll that initiative die just yet. In games with an initiative system, there is this strange moment where non-combat becomes combat. The DM says "roll initiative" and...
It is impossible to roll initiative and then try and think of a way to succeed in the current situation without combat. The fighter will instantly go into attack mode. There is, of course, a lot to be said for being a good player and having a good DM. But I swear those two words create a pavlovian response and the itch for violence, even when it is not the most fun thing the PCs could do. So instead, wait to roll until a real combat situation has dawned. If the PCs are up on a ledge above a basilisk, even if the basilisk sees them, let them act outside of any initiative order until someone gets into a melee with the thing.
6. Destroy the environment. A lot of people will tell you to describe, in gross detail, every attack and wound during combat. However, there is an issue here, and that is abstract Hit Points. Unless you use one of those god-awful wound/blood/fatigue/guts/vitality/blah systems, not every hit means drawing blood, and saying a PC got stabbed in the kidney when they aren't even below half HP yet gets confusing. The other problem is that no matter how many organs pop out of someone, it doesn't make combat more interesting. No one is going to pick up a liver and try beating their opponent to death with it. BUT, furniture and such is easy to break. Everyone knows the parts of a chair, table, chest, etc. If you break those things, PCs will immediately recognize that new, makeshift weapons and tools are available to them in the fight. Also, if your large monsters are not pile-driving your PCs into furniture on the regular, I don't know what you are doing with your life...
7. Meanwhile, back at the ranch. At the end of every round, however you define that in combat, change the stakes. If it is a castle defense combat, have a hail of arrows, or a catapulted boulder, or a battering ram, or a bunch of ladders suddenly become relevant. If you are just in a dungeon with a single monster, have spells light the fungi on fire, have bats fly through the area because of the noise, have the monster's stomping cause loose rock or dirt to fall from the ceiling. Give every round its own little special event so the pace stays engaging.
8. Let the smaller/sneakier enemies hide mid-fight. This is a good escape plan, but also a great way to change the tempo of the fight. A cluttered or multi-walled area lends itself to suddenly disappearing and then stabbing people in the back.
9. Weather, baby. A downpour goes a loooooong way to setting the mood and making cool description easier. Also, wind, snow, hail, sleet, lightning, debris flying through the air. Stop having so many temperate, sunny encounters. In a dungeon? Well, the ground absorbs water, you could potentially have a wet season in a dungeon. Volcanic shafts could break through in certain places. And when all else seems too contrived, magic is the answer for why there is SO MUCH DAMN SNOW IN THIS UNDERGROUND CAVERN!
0. Combat is a drug. And the more you have of it in your game, the less it will impact the players. I recently played in a game where the first session consisted of saving a town from an invasion of kobolds under the leadership of a blue dragon. We had no less than six encounters with kobolds back-to-back-to-back, which I'm sure made sense to the DM, since it was a large town being invaded by an army of kobolds. But I can tell you that I, and essentially every player at the table, was bored by the end of encounter #2. I would have given anything to go help some people escape burning buildings instead. (In fact, I did. I had my character literally jump through a window and into a burning building to help a family, entirely skipping the group of kobolds outside that we were supposed to fight first). Two rules of thumb here. First, build up to your combats, like how the drums build up to the Mines of Moria encounter in LotR. Second, make it big, hectic, and deadly.
A quick aside on deadliness. Pitting a group of level 1 PCs against an ancient red dragon is not deadly, it's a joke. BUT! Pitting them against a group of orcs twice their number in the middle of a gladiatorial arena that has tigers and lions chained to posts at various locations is do-able. The PCs will need brains and brawn and luck, but if it required anything less, it wouldn't be worth including in your fantasy D&D game.