Recently I was able to visit New Orleans. As the plane made its approach over Lake Pontchartrain you are able to see that there are many blue tarps still covering the roofs of houses. The airport was quite deserted, as the number of flights have not returned to pre-Katrina levels.
The area of the city where I stayed was in the 20% that had not been flooded. That part of the city had sustained wind damage. Some buildings are missing windows and are currently being repaired. If you were to ride the streetcar to the end of the line you will go through devastated areas. The citizens of New Orleans seem to be in good spirits though. All were very friendly and most places have reopened. It was very nice to be able to visit the Aquarium of the Americas, a building that suffered much damage in Katrina.
I will say that New Orleans is still fairly deserted, a large portion of the population have not returned yet. It's odd to wander around what was usually considered a bustling city when it's so quiet.
All in all, it will be a slow recovery process but the people of New Orleans are up to it. If you're thinking of visiting, I would say this, be patient as the city gets back to full strength, but don't be afraid.