The tank you play after a hard day, when you just want to relax and have a nice game. Or the one you fall back on, when you are having a bad session and need to cool down.
I'm a fairly new player, during my first ~500 battles I would always come back to the VK 30 01 H: Very simplified gameplay, without much armor or mobility, but with a gun that always hits and always pens.
Now, I've "moved up" to the Dicker Max: Huge alpha, -15° gun depression and epic view range. Read the battle, search for angles, ambush over ridgelines or from cover and be rewarded with that beautiful alpha. Very chill gameplay.
What's your cozy tank?
Edit: Wow, so many posts! Seems like there are a few favourite tanks like T-34-85M, Tortoise, T-150 and TS-5, but basically 100 people give 100 different answers.. interesting!