Houses catch fire someplace everyday for various reasons from natural causes, human error, to arson and many other causes. The time it takes to have something done with the property afterwards also depends on many factors, such as cause investigations, insurance claims, and litigation.
Does it affect the value of your home - no. The value of your home is based on the specifics of your home, market conditions and trends, and market reaction for your type of home and its specifics, ecominic factors, location, etc.
The fire damaged house next to yours is considered an "external obsolescense" meaning a feature made undesirable because of a condition, or conditions, outside the property, which the owner of the property (you) has no control over. External obsolescense is generally considered "incurable", however in your case it would be considered "curable" due to the likely-hood something will eventually be done to cure it.
Does it affect the marketability of your home - possibly - due to the likely decrease in potential buyers willing to purchase your home with a fire damaged home next door.... more