I used to work with the T420/520 and older thinkpads a lot (hundreds) along with a few T420S, and honestly, they're fantastic, well-rounded laptops. There is so much to like about them.
-Fantastic keyboard, with perfectly sized and placed keys, and has water drainage in the keyboard, so if liquid is spilled, there are little tunnels which allow the water to flow through the keyboard, and internals, to the bottom of the laptop, without actually touching circuitry (works really well, but not 100%).
-Incredibly well engineered and complicated internal frame (making it really, REALLY durable, but also a complete bitch to take apart) (less so on the S model, because its slimmer, but still very durable compared to modern crap)
-Great battery life with the extended batteries (T420/520)
-Upgradeable to quad-core i7 processors (second gen confirmed by moi for the T420, doubt the S models support quad-cores)
-Some people are die-hard "nipple" fans, and cant live without it (im not one)
-So, so much IO expansion. Puts modern laptops to shame, and can add even more with a dock.
There are cons to them as well
-Garbage displays (however, you can buy different displays if you'd like, and switch it out for stuff like IPS and touch screen, because it uses a very common display connector)
-Trackpad is garbage and gets work out (however, can be replaced to make it act brand new)
-Extended batteries are annoying a.f to me because they stick outside the laptop (T420/520)
I didn't work with the T430/T530 much, however, it does a completely different keyboard and touchpad (some don't mind, some absolutely hate, I don't mind too much), but are overall still pretty good laptops compared everything consumer based.
Whenever friends ask for laptop suggestions, the first thing I always suggest is either Mac Airs/Pros because they're mostly good (lets ignore the fact that the logic board dies after 3 years because Apple designed that to happen), or used business laptops, because they're just fantastic for the price, and much better than any consumer garbage that you can buy, plus, tend to even have better performance.