The freedom, prosperity, and comforts provided by planetary life will always be desirable. All eyes will be on planets within the green zone--the range of orbital distances from a star that, given the right atmospheric conditions, life could thrive within. Mars is within this green zone, and evidence suggests that it once may have been home to an atmosphere similar to Earth's.
One Planet's Apocalypse is Another Planet's Salvation
A dramatic increase in greenhouse gases would be cataclysmic to Earth's ecosystems, but that is what Mars needs. The most potent greenhouse gas is water vapour, and that is exactly what humans will bring to Mars. By tweaking velocity and direction, we can guide icy comets into a collision course with the sleeping red planet. The energy of the collision will not only vaporize the comet's ice, all the underground ice trapped around the impact site will also be flashed into water vapour. Within a few impacts, a runaway greenhouse effect will occur, melting Mar's latent ice and dramatically changing surface and atmospheric conditions. The type of shock that would kill a living planet is the same type of shock that can revive a dead one.
By the time we are ready to begin terraforming Mars, it may be that the colonies in the Avalon phase have grown too populous to evacuate. An alternative to the ballistic approach is to pump greenhouses gasses into the atmosphere via man-made factories. Just as with a comet collision, destabilizing pollution has its uses, although with dramatically slower results.
Terraforming: Nano Style
By the time we enter the Elysium phase, it is entirely feasible that technology will have developed to the point where nanotechnology is capable of terraforming Mars for us. This would be the preferred approach, as it will allow for direct control over the process, something that the greenhouse solutions lack. What this technology will look like and what the transformation timeframe would be is merely speculation at this point.
Built to Last?
Earth's magnetic field protects our atmosphere from being stripped away by solar winds. Mars lacks this important field and unless a protective field can be induced, no atmosphere humans create will last. The leaching effect may take many centuries, but eventually atmospheric maintenance will need to occur if terraforming is to last.
A Lesson for the Future
Eventually humanity will leave this solar system in search of new and exotic territory to claim. It is likely that orbiting one of the billions of stars will be a planet perfectly suited for terraforming. Any insight we can gain into this process by experimenting with Mars could end up saving a galactic seed ship's inhabitants centuries of time and effort.