Knowing what your opponent is up to is key to devising a proper strategy for attack as well as providing knowledge of what you'll have to defend against. If you know every move your opponent is going to make, you'll have little diffuculty winning the game. Likewise, you need to deny your opponent the same advantage. Luckily, Terrans have a number of options for securing that kind of crucial intel.
Early in the game is where intelligence gathering should begin. At about your eighth or ninth SCV, send one out to find the enemy's base. Once you find it, see what he is building. If he's working on a second Barracks or Gateway before harvesting gas or building more advanced units, you should brace for a rush of low-level units. If he has moved to building more advanced buildings, then you may want to consider initiating a rush of your own.
Following this preliminary probe of your opponent, intelligence should come from two new places. First is the ComStat Scanner add-on for your Command Center. At a cost of just 75 energy, you can have a free look at your enemy's base. You should do this at every opportunity to see what he's up to. Between these short glimpses you should use cloaked Ghosts and Wraiths to probe at the sides of the enemy bases and, if possible, even to slip inside for a closer look. As asways, stay from detectors like Overlords, Spore Colonies, and Photon Cannons.
One of the few good uses for Vultures is as a disposable scout. Simply send it in the base and see how far it gets in the defenses. The other decent use is for laying spider mines that also act like stationary cameras for you. Scattering the spider mines at various points alont known enemy paths will provide you with an early warning system for attack.
On the counder-intelligence side, the Terrans are at something of a disadvantage when compared to the Zergs or Protoss. Unfortunately, Terrans only have one mobile detector unit, the Science Vessel, and it's quite expensive, so you probably won't have many of them. At least one should be placed on full-time patrol duty around the perimiter of your base. In doing so, any cloaked enemy unit will show up on your radar and any of your Siege Tanks should take it out on sight. This is particularly useful for finding any Observers or Ghosts that may have been undetected by your missile towers.
The other key has to do with base design and positioning a web of Missile Towers around the perimiter of the base. A single hole in the web can spell disaster agains a Terran enemy with a Ghost and a Nuke. When playing against a Zerg player, constantly check your workers and other units in the base for presence of a Parasite. If you find one, either destroy it immediately, or better yet, send it on a suicide mission into the enemy's base so you can have a look at his defenses again.
The secret to properly cracking an enemy's base revolves around the proper use of Nukes in conjunction with well-supported Siege Tanks. That's not to say it couldn't be done just with Siege Tanks, but taking out some enemy units and basic defensive structures with a Nuke or two makes it so much easier.
While this sounds easy, there are a couple of different ways to approach the situation and a few diversionary tactics that can help maximize damage and minimize losses. The first way revolves around having a couple of Nukes prepared. For those who are unaware, there's a nice way to have two Missile Silos able to be powered by a single Command Center (though not at the same time). Assuming you have already built one Nuclear Missile Silo from single Command Center, simply lift the center off and set it down again some distance away. Then begin building a second silo off it. While you can't be building Nukes in both Silos at the same time (as each Silo depends upon the center for power), you can have a Nuke ready to be fired in one and then disconnect and reattach to the second Silo where it can then prepare to fire. In this way, you can stockpile Nukes (kind of) without having separate Command Centers for each Silo.
Assuming you have at least two Nukes ready, position Ghosts at opposite ends of an enemy's base. The first Nuke is going to be a diversionary tactic used to draw defenses to the hole it creates (and away from your primary attack location). The second Nuke is going to create a back door for your awaiting Siege Tanks and back-up (consisting largely of Goliaths and Marines for anty-air support, and a few Ghosts for Lockdowns where needed). Be sure to set at lease three or four Siege Tanks in Siege Mode slightly behind what you anticipate will be the front lines just in case you should temporarily have to fall back. Again, every Siege Tank should be withing firing range of one of its brethren for protection. Use Ghosts to lock down threatening Ultralisks, Arbiters, Siege Tanks, and Reavers.
Under the cover of at least a dozen Marines and a dozen Goliaths, Siege Tanks should begin gaining ground in a leap-frogging fashion. Just as the last target is destroyed withing firing range, the tank furthest away in the group should un-Siege Mode itself and slide forward to protvide new targets. While it might be tempting to do so, don't let your support units (the Goliaths and Marines push forward into the base for further action Meghodical destruction and proper support willensure complete annihilation. If you let them get ahead, you splinter your force and risk being repelled.
The first targets should be defensive emplacements such as Sunken Colonies, Spore Colonies, Bunkers, Photon Cannons, and Missile Towers. Following those, structures that produce units directly such as Barracks, Gateways, etc., should be targeted.