Your landlord may have the best insurance coverage imaginable, but that doesn't give your possessions any protection. Renters insurance plugs the gap, protecting what you own up to the limits of the coverage. If a pipe bursts, your insurance doesn't usually cover damage to the landlord's building or the flooring and carpet. That doesn't mean you have to pay: it depends on who's responsible for the flooding.
Renters Insurance
Rental policies don't cover flooding from storms, but they normally cover flooding from burst pipes. Read your policy over to confirm this before you sign. If you bring in throw rugs or a small carpet and a burst pipe ruins them, you're covered. If the carpet belongs to the landlord, your policy won't apply unless the damage was your fault. Rental policies usually cover other people's losses from your negligence.
Limitations
If you have a deductible -- $500, say -- any damage below that figure is your problem, not the insurer's. The same holds true if the damage is more than your policy covers: If you have $5,000 coverage and $6,000 worth of damage, that's $1,000 the insurer won't pay to fix. Another factor is whether the policy pays replacement damages or actual value. Replacement cost covers the cost of replacing the carpet; actual value only pays what the carpet was worth, which may be much less if the carpet is old.
Uncovered
If your policy doesn't cover the damage, the responsibility for replacing the carpet may depend on what caused the pipe to burst. If you told the landlord the pipe was leaking and he never got around to repairing it, you can claim his negligence caused the damage so he should pay for it. When you're at fault -- you broke the pipe trying to tighten a joint, say -- it's more likely you're the one on the hook. If it's just a freak accident and nobody's fault, your landlord's responsible for fixing things.
Considerations
Once the pipe is fixed, take photographs of the flood damage. Even if it's only one room or a few square feet, your landlord may try to claim you should pay for a full carpet replacement. Evidence he's exaggerating will help your case. If the carpet damage makes your home unlivable for a while, many insurance policies provide relocation coverage. The policy pays for you to move into an apartment elsewhere until the carpet is replaced.
