I Like Cooking Smells!. If I go into a house that has the smell of cooking, I always think it is nice. It feels homey to me. It's certainly better than artificial scents, but if you are really concerned about it becoming a stale odor then I suppose you could use incense to clear it out. Just make sure you open all the windows when you are burning the incense...and try to use pure incense, it's a bit healthier than the stuff with chemicals in it.
Leaving grease and leftovers around. My grandma and mom would always be frying pungent fish. Always. Yet the house didn't quite smell like fish .... I'm not sure if it was what helped, but the fan above the stove was constantly on whenever my family cooked, and was even left on while dinner was being served (although that became kind of distracting). I also noticed that most of the homes I've visited that DO have a stale food odor are the ones who tend to leave the food out in the open longer, like the way you would leave potpourri out to infuse the house with the smell; I've also seen some friends' apartments, and the ones that smelled had uncleaned grease spots all over the stove, overhead fan and kitchen, as well as unwashed pans that just sit in the sink. I feel like these factors are more of the culprit for a bad smelling home when they just chill and sit around the kitchen for long periods of time. So the solution I would guess is to clean up and wash really well right after dinner, and let the immediate cooking smells out through an open window before they set in.