I understand some companies allow pilots to call in sick without producing a Medical Certificate or visit a doctor.
That's the case where I work (UK), in fact the national rules are such that your doctor usually won't expect to be asked issue any paperwork for sickness of 7 days or less. For short illnesses (e.g cold/flu) you just ring in when sick, then ring in again when fit to fly - but you do back it up with a computer generated form on return to work and if you are continually and frequently absent the company will start looking at your record with interest.
Long term injury and/or sickness of more than 7 days may well require a visit to a doctor and may involve extra paperwork.
( Edit to add - must speed up my typing - in other words what Dave said)