Sure they can; like most thing it all depends on what you want to pay for. I have a number of friends back in CT who have whole house, auto start generators (for 4000+ sf houses) with a huge buried propane tank to keep the thing humming for weeks. Of course, price tag for that set up can approach $20,000.
After Hurricane Irene I opted for the 5500-watt, gas fired Home Depot generator for $500. Hired an electrician to install a separate panel and do the wiring to the main box and set me up with the right power cord and I was good for 4 separate multi-day outages afterwards; one lasting six days. I ran my well, septic, heat, and general house lights/power, oven. Had to be a little careful about not running too much at once but in general had pretty much everything working except laundry.