Technic: A collection of mods that focus on advanced technology. Contains: MineFactory (automate everything!), BuildCraft (engineering, automation, heavy industry), IndustrialCraft (machines, electrical engineering, advanced technology), Forestry (advanced farming), RedPower (advanced Redstone engineering and programming, art), ComputerCraft (Computers), Equivalent Exchange (Alchemy), ThaumCraft, and more.
Tekkit Classic: The multiplayer version of Technic.
Tekkit Lite: The Tekkit Pack, now with less calories! Actually, it has more mods, it just uses less intensive back-end software.
The Big Dig: A pack focussing mainly on world generation, adding loads of extra ores, and even other worlds to explore. Contains: MineFactory, BuildCraft, Forestry, Equivalent Exchange, Mekanism (various extra tools and devices), Dungeon Pack (various naturally generating dungeons), Dimensional Doors (doors to other dimensions, duh), MystCraft (travel to other worlds), various ore-related mods, and more.
Voltz: An in-depth system of electrical engineering. Also, ballistic missiles.
YogCraft: A custom mod pack made by and for the Yogscast, designed to combine Tekkit and Voltz, with some other stuff thrown in for good measure.
Hexxit: A More adventure based mode. Various mods are installed such as Twilight Forest, and Battle Towers to start.
Nuclear Reactors. If properly designed and maintained, they can easily power entire bases with surplus. If improperly designed or maintained, they can very easily destroy most of a base.
The Catalytic Lens in Equivalent Exchange. It fires projectiles that destroy large areas of blocks, then teleport the resulting broken blocks back to you. Above and beyond the best mining tool in the pack.
Beam Spam: The Mining Laser, especially in Scatter mode
Bee Afraid: Averted with the Bees in Forestry: Although some types can be dangerous, most of them are actually useful.
Played straight in early versions of Tekkit Classic, for permissions reasons. Forestry was originally included in the pack without Sir Sengir's permission, so in retaliation Sengir made Beehives start slowly destroying the world around them. Forestry was not in Tekkit Classic for very long.
Colony Drop: The Falling Meteors Mod. Meteors in Hexxit can be real threat as it may destroy the player's base if out in the open unless one gets Meteor Chips from Already fallen meteors and from meteorite clusters underground to create the Meteor Shield. However they yield valuable resources. One can even summon meteors if they use a specific crafting formula, the summoned ones will bypass the shield though.
Dynamic Entry: Battle Tower Golems may begin the Boss Fight with them by smashing through the ceiling from the floor above instead of waiting for the player to initiate the fight. Ogres will happily destroy anything in their paths to get to you. (Fortunately, they don't jump or climb well.)
Equivalent Exchange: The mod Equivalent Exchange. Specifically, it assigns each item in the game a value, and items can be absorbed and transmuted into any other items with equivalent total values.
Fantastic Nuke: Voltz. Specifically, the mod ICBM. Where to begin? Bombs that create antigravity fields, bombs that scatter blocks around rather than destroying them, bombs that put fire everywhere, bombs that put ice everywhere, bombs that put poison everywhere, bombs that create portals to the End, bombs that create Black Holes, bombs that deal 2.14 million damage to everything around them, bombs that repair rather than destroy... and actual nukes.
The Regenerative Explosives ("bombs that repair rather than destroy") can actually be the meanest. Rather than visibly destroying large areas of the world, they take those areas of the world and reset them to their initial state. Which means that anything you or your enemies had built there... never even existed to begin with.
Thunderbolt Iron: Frezarite and Kreknorite from Meteors from the Falling Meteors mod can make exceptional armor, one can also find Frezarite or even Kreknorite armor as drops from Infernal Mobs or in Battle Towers.