In a nutshell, there aren't really any limits - take one human with money to spare and a risk at hand and one insurance company willing to make a bet, and you have yourself a deal.
There are a lot of different reasons why a person may choose to get insurance cover, and while none of them would surprise you lot, there are some notable policies hanging around for eventualities an insurer has deemed unlikely enough to occur, to cover.
Some of the Hollywood and international sporting crew have taken to insuring their saleable features - hair (pro footballer Troy Polamalu), buttocks (Jennifer Lopez), smiles (America Ferrera, Ugly Betty's leading lady), voices (Bruce Springsteen), moustaches (Merv Hughes), chest hair (Tom Jones), and legs (Heidi Klum, Mariah Carey). People also insure their pets and their funerals, but this is old news, and both of those insurances are more like a co-payment plan/savings plan than true insurance.
This is where it starts to get interesting
You can also get divorce insurance, with one such policy available in the USA called WedLock - it's a casualty insurance offering a payout once the marriage dissolves. The policy is US$16 per month for every $1,250 in cover, but with some caveats - a policyholder must 'invest' four years before a policy will pay out, but with an extra premium of $250 per unit for each year the marriage exceeds four years. The policy doesn't really seem worth it - four years is a long time if it isn't working, and if it is working, then you could potentially be paying an outrageous sum for a happy marriage. Over a 10 year period with 10 units of cover, the cost is US$19,188 with a payout of $27,500.
So who invented divorce insurance? A guy by the name of John Logan set up the company after his marriage went down the gurgler. In a Time article, Logan reportedly wouldn't tell how many policies he'd sold so far, but did say that he was surprised at just how much some people were spending on this insurance, with some paying premiums of over US$1,000 per month.
The policies are being bought not only by the wedded, but by concerned friends or relatives in secret or as gifts, though the bride or groom must be the beneficiary - it's not a horse race, and nobody else can receive the windfall when the sometimes inevitable occurs.
Another insurance which may be (arguably) more sensible is wedding insurance that covers the day of, and any disasters that may befall nonrefundable preparations (but not the actual couple).
A photographer took out a policy to protect himself from his prize model getting married and no longer modelling - which she did, but only after the policy had expired.
Lloyd's of London has insurance policies named 'improbable insurance', which means you can take out insurance essentially the same way you would take out a bet. One such example is where you insure against the improbable occurrence that you/your lover/your co-parenting partner become pregnant with more than one baby. Another Lloyd's example is insurance cover against one (or two, in some policies) of your employees winning lotto and leaving your employ. Lloyd's also wrote an actual policy for a whiskey company, Cutty Sark, who were running a competition for the capture of the Loch Ness Monster (you know, just in case).
Then there's outer space issues that enter our orbit - asteroid or meteor cover. This branches into apocalyptic fantasyland. If an asteroid or meteor hits earth at such a clip that it causes enough damage to warrant the insurance policy, the likelihood of a payment ever being made is slim.
There are also policies that cover for supernatural attack and alien abduction. What's cool about the supernatural attack cover is that all you have to do is provide proof that you were attacked by a ghost or ghoul, and the money is yours! Could Judgement Day be put into this category? God also has a part to play in another form of (now defunct due to complaints) insurance - immaculate conception cover - which covers the birthing costs of the second coming of Jesus Christ.
Alien abduction cover is popular, with over US$10 million in policies written, with frequent abductees able to get higher payouts. Again, all you have to do is prove it, and if you can, US$1 per year for a million years could be yours. The St Lawrence Agency in Florida says they have paid out at least two claims.
The American version of Who Wants To Be A Millionaire is actually insured against someone actually winning.
Turns out, you can insure just about anything, especially in America where empirical data and common sense doesn't seem to count for much when it comes to insurance.