I bust my way through but I take soldiers together in teams, send in high reactions first, go around important corners with high time units, and end turns at good ambush positions. I've got a few strategies for tackling each UFO type:
Medium Scout
* Wait 2+ soldiers outside the door and end turn. Optional: park tank in front of the door so they can't get out.
* Bust high reactions soldier in and start shooting, if that one survives, stop with enough TUs to step aside and let someone else inside.
* Prioritize targets by weapon type and facing. In armor, heavy plasma is highest priority weapon. Without armor, plasma rifle is highest priority weapon (in my mod--in vanilla heavy plasma is still highest priority).
Large Scout
* Get 3-5 soldiers to the door and end turn.
* Move them inside and split teams down toward either door, end turn with reserved TUs and hanging to the side of the door to prevent mutual surprise. Any odd unit with low TUs/energy waits in the middle to replace a lost soldier.
* Move one team in to peer in on the navigation room. Any aliens spotted and you check their facing to determine which team to fire upon them first. Attack from behind them.
* End turn hiding around the corner from power source room. On last turn enter power source room with at least 2 units available and check behind the power source.
Abductor
* Run 2-6 soldiers into the entry room. Inside/outside the door is unimportant as long as you have a good ambush position and reserved TUs. Bring minimum 4 soldiers, but 2 can enter early to clear medic's room.
* Medic room is a TRAP. Expect heavy TU wastage getting past those tables. Take ambush positions at the far door.
* Rush out into the halls and check around the corners, then pop back and wait in the first hall segment. You'll probably find empty corridors but if you see an alien, you'll still probably be fine. Shoot it if you have the TUs.
* Have one soldier check the power source hall just in case (saw an alien there only once), then take 2-3 soldiers towards the lift. If you have over 4 soldiers inside, leave a team guarding the entrance to make sure no aliens escape. They can become backup to replace casualties. Take positions around the lift with reserved TUs.
* Take a soldier with high reactions and high TUs up the lift and turn full circle. Bring all lift team troops up and start taking ambush positions in the hall.
* Move through the hall till you get to the navigation room (about 2 turns of movement) and set up just around the corner.
* Bust in the navigation room and finish this.
Harvester
* I've done maybe 2 harvesters in all my years of playing X-Com. I have no strategy. I'd beaten the game before I even knew Harvester was a ship type. First time I heard of it an engineer had given the details. I didn't actually see one until later when I played the collector's edition.
Terror Ship
* TANKS (PLURAL) ARE NECESSARY UNLESS YOU WANT TO SEE TERASHELL SHOT IN THE BACK!!!
* Seriously. Don't get cocky. Prepare to throw a tank away. This is the kind of mission where strategy makes the difference between 200 elerium and your favorite soldier getting put down like a stray at the humane society. If you lose a tank here, consider that a small victory. Alternatively rookies are cannon fodder, preferably in power suit (to absorb more hits before they die).
* Bring some big teams to the doors. You'll fight a lot of aliens on the way to the ship. Take your time getting there. Usually they aren't running in and out the door so time is on your side here.
* Take 1-2 tanks in on each side and check around the corner for aliens. Leave tanks facing in toward the center (without moving through the corridor) while 2-3 soldiers per side wait just inside the door out of sight.
* Move tanks through the corridor and expect to be shot. There are large openings overhead leading to where the terrorists hang out. If this is sectoids, you may see cyberdiscs hiding up there ready to pop your tanks. Soldier units may also wait up there to ambush your units as you come through. If you have hovertanks, take them up through the hole to make sure it's clear up there and stage them looking towards the second floor door into the terrorist bay.
* Move soldiers around the outer ring and stage around the door.
* Pop in to power room and check multiple angles to make sure no aliens are hiding behind power sources. Reserve lots of TUs with soldiers facing the lift.
* Bring soldiers up and fan out to check the hallways. Most likely place for aliens to be is navigation room. If you clear that and there's still aliens, they are probably outside the ship.
Supply Ship
* bring two teams of 2-4 soldiers to the ship, one team per entrance. Stage with reserved TUs just outside of door.
* Bust in and get to the corner, check around corner if you have enough TUs, and wait in ambush positions.
* Check in power room for an alien. Looks clear? Step to the side. It's in there, hiding behind the power source.
* Reserve TUs near lifts, also beware of aliens lurking in the corridor between the lifts.
* Team 1 goes up to second floor, Team 2 goes up to third floor. Team 1 is in high danger, Team 2 is safe. Pick your moves with Team 1 carefully here.
* Team 1 should open the doors and peek out of the lift room, and reserve TUs in good ambush positions. Aliens love to come from around the rooms in the midsection to shoot at your soldiers. Sometimes they hide among the food containers. The rooms are generally empty but aliens will hide behind them and pop around the corner to shoot at your soldiers. So cover ground quickly but keep soldiers in positions where they can find a line of fire to bail out a frontrunner with low TUs who found an alien.
* Team 2 should split up and send one branch around the back while the other branch goes forward to the navigation room. Forward branch should have high reactions, but it's also a good place to train rookies.
* Team 2 danger ramps up here. High chance of meeting alien in back corridor. Aliens will pop out of navigation room and run back inside. Wait around the corner out of sight.
* Make sure you have at least 2 by the door, then get your rookie/breacher into navigation room and shoot at alien. Step out and let second soldier in to continue the carnage as needed. Leave the frightened navigator hiding in the back if you have to. Do not attempt to fire at it past the chairs and do not end turn inside that room. It'll sit back there and probably panic. Just run in with full TUs and dispatch it next turn.
Battleship
* I may just not be good at these but I tend to lose a soldier or two on a landed battleship.
* Run 6-8 troops and up to 1 tank to stage around large lift. Other tanks should scout the landscape.
* Send tank or breacher to second floor and turn full circle. You'll probably sight several aliens. Consider your moves carefully here and prioritize kills. Try to fan your troops out by the end of the turn, with 1-2 in third floor lift room and the rest on second floor checking the halls. Getting as many kills as possible is more important than reserving TUs. Sometimes getting in a safe position is more important that reserving TUs. Expect to not find ambush positions.
* Once second level is secure, start checking the individual rooms and the four first-floor power rooms. Tank can stay and patrol the main halls on second floor. Move excess troops up to third floor until you have 3-4 soldiers on third floor.
* Pop soldiers out of third floor lift room doors just to check down hallways, then reserve TUs in the halls in teams. Make sure any soldier on third floor has another soldier close enough to run to their position and fire weapon within one turn.
* Run soldiers down the halls and check rooms, but send at least two to the navigation room. Expect aliens inside the navigation room and in the halls. Other third floor rooms are probably empty.