Microscope halogen bulbs should never be touched with bare fingers when they are exchanged. The oils (and other substances) on the skin deposit on the glass of the lamp. The heat of the lamp will cause these oils to burn in and form a darker region of deposited carbon. These regions absorb more light energy from the lamp and will therefore heat up much more than the rest of the glass bulb. This creates tensions in the glass of the bulb, which might result in its breakage.
Halogen bulbs are especially sensitive in this case. The bulb contains a tungsten filament and contains a halogen gas. Due to the high temperature of the tungsten filament, some of the tungsten evaporates and deposits on the inside surface of the glass bulb. In a process called the halogen cycle, the high temperature, in combination with the halogen gas, causes the deposited tungsten to be removed and redeposited on the filament. This greatly increases the life span of the lamp and also makes sure that the color temperature of the bulb stays the same over its life span. The higher operating temperature is also responsible for producing a cooler (more blue) color spectrum. Deposited grease on the glass will cause an uneven heating and therefore might also interfere with the halogen cycle, which removes the deposited tungsten.
The more “traditional” incandescent microscope bulbs also have a tungsten filament but operate at a lower temperature. The deposited tungsten on the inner glass surface is not removed and the color temperature changes over time. While it is generally not advisable to touch any bulb during replacement, the incandescent bulbs are much less sensitive to deposited grease, due to the lower operating temperature.
LEDs do not have this problem. They have an entirely different mechanism of generating light and only heat up minimally during operation.