Oh, man. First of all, no 1 skill will do it all in Skyrim, so some of these combos are with other trees.
Flames: Don't just hose them, but hit them with pulses as fast as possible to stack up the Afterburn effect. Less XP, but a lot more DPS for those tough bosses. Also, Draugr are the best sparring partners for Destruction. Crypt dive for the first few levels to get up to Augment Flames.
Firebolt: Like Flames, you can rapid fire to stack up Afterburn, but with 25 more damage with each hit. Excellent single target damage dealer, but doesn't spread it around like some others. With Impact, you can cast 2 or 3 more singles before you have to stun them again, and get more bang for your buck.
Ice Spike: Slows them, so you don't have to Stun them as often, and can run circles around the melee.
Lightning Bolt Hit Scans, so you don't have to lead targets, you won't get as many off, but you won't miss as much either. Good to proc Disintegrate so they're weak against follow up shots (Especially nice set-up for a Spellsword's Critical Charge.) Can 1 shot a Flame Atronach, hopefully with them clustered in the blast radius. (Even your own!)
Fire Rune: A "Poor Man's Fireball" until you get to Adept, the Strategist can also cast
one, and let his Magicka recover before kiting the enemy into it. Also blasts Draugr out of their coffins, you can do this at the end of proving Honor before you pick up the Fragment, and skip the last fight entirely. (Also keeps Frakas from stealing all your XP.)
Ice Storm: Probably the best offensive spell in the game. You can kite armies into a line to hit all of them, fatigue, and Slow. With Impact/Deep Freeze you can add Stun/Paralysis to the mix. Can also be comboed with Flaming Familiar to detonate on contact (or Runes work too) and hit them with both Elements. nothing is significantly resistant to both.
Flame/Frost Cloak: Storm Cloak looks nifty, but the Magicka Drain effect is less than stellar because other mages tend to fall back spellcasting instead of engage you in the AoE. Not a decent replacement for Weapons in a melee, but you can run circles around them (Unencumbered Altmer are the fastest.) to hit people with Afterburn/Slow en passant. Spellswords, Battlemages, and Sorcerers can use this even more effectively with Weapons/Armor.
Incinerate/Icy Spear/Thunderbolt: I don't use these, because I can do more damage with 3 Bolts, and let my Magicka recover more in between. If you're just Stand&Spam, you pretty much have to make Destruction free to be effective in anything more than a duel. None of them AoE to multiply Targets, even. Thunderbolt, and Ward Absorb is my "I don't need Dragonrend" combo. It takes timing, but you can shoot them down, and block all their shouts.
Wall Spells: Here's yer damage! Each pulse does a total of 1000 damage unaugmented, if you can keep them in the AoE for the duration. Wall of Storms glitches Impact, however, so it won't stagger as long as they're still sparky. Unrelenting Force stuns them down long enough to pulse a puddle at their feet, and switch to Impact for keeping them there. The fastest way to kill a dragon I've found is Dragonrend, then hose down their broad footprints with all 3 elements. That's 150 damage per second for every spot they cover on the ground. If you side straffe, you can get every nook, and they tend to turn instead of crawl after you. You can also cast them at your feet while running away to kite Giants over. You can make do with just Fire, and Frost. The cold one slows them down for kiting, and also drains dragons' Stamina so they can't take off for your to Dragonrend them again. For my Perks, Shield Bash, or Windshear are the best ways to keep them stunlocked in the AoE...
Absorb Health: (Vampires) Benefit from all Fire enhancements, including Ahzidal, and Aspect of Terror.