I'm uneasy about the term hypermiling as it conjures images of people holding up traffic or doing dangerous things just to save a few pennies.
However, I do drive with economy in mind (while enjoying cars as they're meant to be enjoyed when the mood takes me).
Obviously my car is rather predisposed to economy. I've done about 9500 miles in it since March at an average of around 72mpg imperial, or about 60mpg US. My current tank is over 80mpg imperial, though since my new job started my mpg has gone down due to the commute - high 60s imperial is the norm.
No modifications beyond what the car already offers. Tyres are at 45psi after some experimentation. 35 made the steering feel mushy. 40 was fine, 45 is better without sacrificing how the car grips and handles. 50 is too much - ride and handling deteriorate and the car squirms under hard braking, which isn't pleasant.
Everything feels better when the car is warm though. The tyres are better with some heat in them, and the battery offers more assistance after maybe 30 mins of driving.
I don't do neutral coasting, as it's counter-productive in a car that recuperates energy when you coast in gear. However, under certain braking pressure and in neutral (or under 19mph in neutral) the engine turns off entirely, which is even better. Perfectly safe too - the electrical system maintains steering assistance and the brake servo.
No aero mods either - the Insight has its own