My times are from Nashville to Houston (MS).
Option A: The Natchez Trace
This is the fastest (if you speed) but also the most boring and without scenery or pissing areas if you need to stop a lot. Get on the trace however you want, and then get off at 412 (the hohenwald exit) and head east toward columbia, where you get on I-65 and it's a straight shot to Nashville at 70 mph. I've done this trip in 3.5, but that was seriously hauling *** at around 100 the whole way at 2 A.M. on the trace.
Option B: Through Bama
Lately I've been taking this route home because after driving the trace to work in Tupelo for several years I am tired of it. Many more stops but does take right at 4.5 hours since it isn't a straight shot no matter how fast you go. Basically this consists of going east or northeast as much as possible until you can get to 65. The way I take it, I get on 78 and head east until Hamilton, then head up 43 until Newberg or so, and get on 24 and head east until Decatur, where I jump on 65.
Option C: Through Corinth on I-40
I rarely take this, but if you don't want the trace and don't know your way through bama this is a pretty good route though it takes the longest at around 5 hours. Basically you go up 45 until Jackson, then go east on I-40. The stretch on I-40 from Jackson to Nashville is pretty bare but it is 4 lane and 70 mph. If you are farther north, I'd recommend this way.