When the heat kicks on, if you don't have a humidifier built in, the heat and the cold weather outside makes the air very dry. People experience the effects of this as well often in the forms of congestion, dry throat, and dry skin. I also notice TONS of static electricity. I can't pet my cat without shocking her if I don't run a humidifier in my apartment.
I use a Honeywell warm mist humidifier in my main room/bedroom and a Crane cool mist in my bird room. I run them 24/7 once the heat turns on, and they're both filterless models, so water treatment tablets and weekly cleanings are important to stay on top of. I think they're pretty important, but for many years (especially living with my parents), I never had one. Considering how sensitive birds are, I imagine anything I can feel, they feel too - but exacerbated. Their lungs are more efficient, but most species aren't well adapted to dry environments. Even if it's not an absolute necessity, I think it provides more comfort for everyone in the household during the winter months.
eta; the Crane is new that I just bought this year. Before this, I had a much smaller Sunbeam humidifier (a little cubicle sized one), but both Sunbeam and Honeywell have served me well for 3 years now.