Terran vs Terran - Breaking Siege Line Efficently

Edit: Wings of Liberty answer only, this is outdated in HotS!

The most used tactic when you go bio vs his siege tank push is to flank his siege tanks with stimmed marauders, stutter stepping towards their dead zone as fast as possible while still shooting.

You want to apply pressure from the front at the same time to force his marines in a defensive position in front of the tanks, otherwise they'll just kill your marauders off.

If however you went mech, simply having your siege tanks sieged up will zone his siege tank push enough to force him to make the first move, thus taking more damage. He'll most likely try to flank you, so be prepared to deal with it somehow. You'll want to mass enough vikings to zone his medivacs (denying his vision) and provide vision for your tanks instead, and to expand behind your siege tank line to get enough resources for a skyterran transition (battlecruisers with raven and viking support).

Another tactics that was not mentioned is : fill a medivac dropship with marines and drop them right on top of the siege tank. Of course you cannot do this safely if the opponent has air control or has a lot a marines near his siege tank but i have seen it work in pro games so it should be possible for us to pull it too. This will sacrifice some marines but will also make the other tanks kill their own tanks.

You can use the following tactics:

• Surround the siege tanks with MMM and attack all at once (similar to Zerg). Because of the huge concave only a few units of you will die.
• Scan regularly and try to catch his tanks while unsieged.
• Create some Ghosts and some Nukes and position your Ghost so he cannot kill him with his sieged tanks. Basically only the border of your Nuke should overlap with some of his tanks. Once he unsieges just cancel the Nuke with ESC and stim right into his tanks.
• Create about as much Tanks as he has and add a bunch of Vikings. Try to get Air superiority and kill his Medivacs. Now position your Vikings between his and your Tanks and wait. After a while leap a few tanks into fire range. He cannot attack you because he lacks the vision. Once your Tanks are sieged you can attack him because of your Vikings.
• Get Vikings and either Banshees or Battlecruisers with some tanks. position your air units between your hand his tanks and kill them. If he unsieges chase him. If he attacks your air units with Marines, just pull back into your tanks.
• Build some Thors and attack with your Thors at the front, MMM should follow.
• Get some tanks with MMM and siege up right next to him. Wait a while and then load up all your Medivacs to doom drop right into a vulnerable position like his base. He will loose a lot of his units if he tries push, because of your tanks. Once he backs off, load your units into the Medivacs and retreat or attack another position.
• Get more expansions than he has and build more production facilities and just wait. He has to attack eventually. If he destroys your army just create a new one before he reaches your base.

If you like MMM I would suggest using Ghosts, but it takes a while to get your first Nuke ready.

If you are a beginner, then I would suggest going Tank, Viking with a few Banshees.

Using ravens has always worked for me. Dropped Auto-Turrets near their tanks to cause splash damage death or to atleast soften them up.