I believed they were destructive and invasive, but it seems they eat bugs.
Destructive? Yes and no. They are destructive if you have a pretty lawn with a lot of bugs underneath it, especially but not limited to grubs. They are very beneficial in nature for turning over the soil and helping to plant seeds as a result of their efforts. They consume a lot of destructive bugs and their larvae.
Are they invasive? Yep, they are naturally invasive in the sense that they have expanded their range (no doubt helped somewhat by people). Their spread across Texas was very well documented in the 1900s, 'dillos leaving the Rio Grande Valley sometime after 1900 and pre 1905. Their progress was documented quite well as to what years they turned up in what counties. Strangely as I recall, there was a leap from Texas to Florida without occurrences in between. It was suggested that armadillos might have managed to spread to Florida via vehicular transport, most likely completely unintentionally. However, Florida and the whole Gulf Coast are well within the armadillo's temperature range and so it was only a matter of time before they go to Florida. Their spread west has been limited by a lack of moisture.
What limits the little guys northward is temperature. They do not thermoregulate well. While they have managed to get a toe-hold in some northern states, they often tend to lodge in the winter under buildings and such that provide heat and protection from the lower temperature extremes.
And the ones with leprosy seem to mostly be in LA, for some reason.
Based on my mammalogy courses, this is because there was a leper colony in Louisiana. Leprosy, or Hansen's Disease, is zoonotic between armadillos and humans, both ways. One of the early cases connecting armadillos to leprosy was that of a boy outside of Houston (some small town) who attempted to develop his running and catching skills for football by chasing down the little guys and catching them (much like McGunner). He contracted leprosy. Then there was a long investigation as to how he got it...resulting in testing of armadillos since the boy had the somewhat peculiar hobby of chasing and catching them. Tests were positive on some specimens. It was later determined that many of the new Texas and Louisiana cases were by people who were extensive handlers of armadillos, such as those involved in racing them, eating them, and making souvenirs out of their shells.
It is believed that armadillos came into contact with leprosy contaminated remains in some manner and hence contracted the disease as a carrier as leprosy does not have the degenerative effects on armadillos as it does humans. It was transferred between armadillos and eventually to some humans. There are some rodents that can carry leprosy as well, BTW (mostly, but not completely limited to the Old World). The contaminated remains might have been simple sputum that the armadillos foraged through during their normal activities. Note that the Louisiana colony was in place from before armadillos was documented anywhere near Louisiana (1896) and didn't close until 1998/1999 with residents allowed to stay on for up to 3 years.
http://www.waymarking.com/waymarks/WMEMV
http://linkinghub.elsevier.com/retrieve/pii/S0190962283702069
Note that the actual source for leprosy in armadillos is actually unknown. For example, see
http://www.jwildlifedis.org/cgi/reprint/23/2/220.pdf
Note that there are about 150 new cases of leprosy in the US each year, but few of those people have anything to do with armadillos.
http://www.statesman.com/blogs/cont...008/11/10/leprosy_seen_in_texas_louisian.html
Note that the concern over infection is a bit overblown as some 95% of the population is not even susceptible to leprosy.
http://www.hrsa.gov/hansens/
People often consider armadillos stupid because you can do things like walk up and touch them for counting coup (noted above...a fun game I have played many times). Armadillos don't have a lot of fears from normal interactions with humans in that sense because their shells offer so much protection. They have poor eyesight, but excellent senses of smell and hearing which are used to detect their prey.