Most of the folks who suffered flood damage recently - for example in Lyons, Longmont and nearby towns here in Colorado - did not have flood insurance. Mainly this is because they don't live in recognized "flood zones." Those people are in the (further) unenviable position of having to seek government assistance or make good their own losses.
Some standard home owner's insurance policies provide limited funds ($10,000 is typical) for backed up drains and resulting damage. Water seeping into basements generally is not covered. Of course whether there is any insurance coverage, how much, and the details, requires a reading of applicable insurance policies. A phone call to the agent should be made ASAP too.
We litigated a case out of Lyons not that long ago where a neighbor had altered the drainage on his property, resulting in a massive amount of water/flood damage to our clients' house following a particularly heavy August rain storm. The jury agreed with us and awarded substantial monies to cover our clients' losses.
The bottom line is that, absent insurance or government assistance, unless you can show that someone else negligently or knowingly caused water to move onto your property and damage it, little relief is available.