This is what renter's insurance is for, in case there is damage that is your fault or that the landlord is not obligated to pay. If you have insurance, contact them to at least report the incident, you may ultimately make the claim directly on the landlord's insurance. And speaking of your landlord's insurance, ask for his insurance information.
As for ultimate responsibility, a lot will depend on the terms of your lease, and the foreseeability of the damage by both you and the landlord. If a lot of a value was lost, you may want to contact a personal injury/insurance attorney to discuss your options.
If this response was helpful, please mark it as helpful or as a best answer. The response provided herein is for informational purposes only and is not intended as legal advice, nor does it establish or intend to establish an attorney-client relationship. You should always speak with a licensed attorney regarding your legal rights before taking or not taking any particular action.
There's no guarantee that a pipe will or won't burst as a result of its age. Just because the pipes are old, doesn't mean that they're faulty or about to burst. Maybe your landlord would be liable for damages if it could be demonstrated that he was negligent in ignoring a pipe in imminent danger of bursting.
Renter's insurance is designed to protect personal items in events such as these. If your renter's insurance company feels the landlord is at fault..then presumably your insurer will take appropriate legal action.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.