The areas on the south side don't have as much crime as they used to because the Robert Taylor housing projects are pretty much gone from that service area, which is roughly wedged between the Red and Green lines. This isn't to say that everyone living in them was a criminal but just that there are less people using the service in general, so of course there's going to be less crime. I would hypothesize (though I don't have actual ridership numbers in front of me) that the Green line took a harder hit, as it lost owl service some time ago, there are long gaps between stations with no visible community demand to fill them, and trains pretty much top out at six cars (the East 63rd branch isn't even capable of holding 8-car trains and I've never heard any proposal to fix this).
The Green Line's situation was worsened (in my opinion, of course...) by the Rev. Arthur Brazier and The Woodlawn Organization (T. W. O.), who led the charge in the mid-90s demanding that a good chunk of the East-63rd branch be torn down, to spur on development (how that would work is not clear to me). Years later there's not a whole lot going on over there, with lots and lots of vacant land that T. W. O. probably hoped would be built on. If Chicago gets the olympics (much of which will be staged in nearby Washington Park), that'll probably gentrify the heck out of the cottage grove neighborhood and price most of its residents right out of their homes. Here's roughly how I think it'll boil down:
1.) If Chicago does get the games, developers will come in and put up new residential housing and rehabilitate any vacant buildings they can get their hands on, make a fortune leasing them during the games.
2.) The developers will then sign long term leases or sell their property outright after the games. The majority of those renting/buying will have higher income than Woodlawn's current residents. Higher income residents will be the most likely to move in here, because they can afford automobiles - which they will need, because service on the Green line isn't that great and a good chunk of it was torn down.
3.) Property values in the area will increase in general, and places like Starbucks will start popping up on 63rd street, to cater to the new higher-income residents (probably either "yuppies" or college students at the nearby U of C). 63rd street will once again be a "bustling corridor."
4.) Landlords who didn't get bought out before the Olympics will realize that they, too, can get more for their property and will price existing Woodlawn residents out of their homes. At the same time, some low-income homeowners will be priced out of them due to increasing property taxes.
5.) Sometime down the road the Cottage Grove/Woodlawn area will wind up looking like Wicker Park. Around this time, new residents will start grumbling about how the CTA service is inadequate, which will result in a push to extend it back eastward...
I think it's pretty much intevitable that that section of the south side will improve. It's just a shame it'll displace most of the current residents in the process, mostly because an overly-vocal few proclaimed that the "L" wasn't good for them.
That old car might be worth money!