Is it possible to fill abandoned buildings in SimCity?

An abandoned building will eventually be reacquired if its problems are resolved. You can see why the building was abandoned by clicking on it to bring up information that building.

In many instances this will be a reason like the building having no water or power, there not being enough jobs within commute distance, pollution or backed up sewage, or the building being damaged by fire.

Abandoned buildings will have a negative effect on the land value of nearby buildings, and have an increased chance of catching fire. Keeping abandoned buildings around over the long term will drive down land value for the surrounding area and it is usually recommended that once the building goes 'dark' (visibly darker than the surrounding buildings - like the one in your screenshot) that it has begun to decay and will soon reach a point that it is better to bulldoze that building to prevent it from causing damage to the value of the surrounding buildings.

When you activate the bulldozer tool, all abandoned buildings of any zone type will begin flashing with an orange symbol with a line through it to make them easier to locate.

To summarize and add to the good and accepted answer. Abandoned buildings can possibly be brought back to life, but it takes a long time. Especially, comparing to how fast they can be abandoned if necessary conditions are not met. They can be brought back from any condition (from simply vacant to damaged by fire), and, possibly, it takes different amount of time given the same demand (or higher threshold of demand) to get repopulated.

Aside from negative implications of leaving abandoned buildings standing, as outlined in another answer, it is possible for them to fall into such state of disrepair that they completely collapse (it takes a long time as well), turning into pile of rubble further driving the land values down, and contaminating the environment. There could be additional icons associated with such ruins (for instance, indication of toxicity), and they should be promptly removed.

Abandoned buildings and ruins can be easily identified in multiple views, but most convenient way to do so is by using the “Bulldoze” tool. The amounts of such buildings would be displayed in the bottom right corner. And they can be seen on the map as a bulldozer for ruins (left side of the image below), or a boarded-up house for abandoned buildings (right side).