Non destructive forks will just result people having different accounts of what transactions are confirmed or not. Your coins will still be there.
Tangents aside, this is interesting. So suppose Alice has 100 BTC and she's running one client, can she send it to bob who's running a different version?
Well, yes, but it may or may not mean anything.
You have to realize that when you "send" a bitcoin nothing actually moves. It's not like you send a file from your computer to a recipient computer. With Bitcoin there is a public ledger in the cloud that contains info on where all the bitcoins in existence are (which addresses). So when you send a bitcoin all you're doing is telling the cloud to record that you've moved coins from your address to some other address. The cloud ledger is called the block chain.
Bitcoin is a protocol, just like HTTP. That means as long as you do things following the protocol you can experience a result. You can access websites on a computer with a web browser, or with a mobile phone app, or something else invented in the future like a robot. So with Bitcoin if you follow the protocol you can have a miner recognize and confirm your transaction (record it in the ledger) as valid. The only question, then, is which public ledger is the "right one" if different miner groups produce different ones? That's what a fork is, a situation where more than one possibly valid copy of the block chain exists.
Users then have to know which block chain to use, because technically both are "valid" (conform to the protocol). Also groups of miners can support both chains, by continuing to build on them. For users that would result in not knowing if transactions sent and received were actually confirmed (forever into the future) until the chains grew sufficiently apart. Their coins would be spendable on both chains until contradicting transactions happened. So for merchants or anyone accepting a payment they would have to know which version to honor as in step with the rest of their money transacting group. Externally, the price per bitcoin might, for example, be cut in half because everyone owning bitcoins could spend them twice, once with each version of the block chain, and different merchant groups might accept different versions.
So economically a hard fork can be extremely messy and confusing for a market. The bitcoin Bob received from Alice might be spendable at one shop, and not at another one next door, or it might not be accepted by anyone (what happens when one fork strand dies).
However, since nobody wants such a mess it's unlikely we'll ever see the well defined split of enough hash power to cause a fork. It's better for all if everyone remains on the same page. Still, a hard fork is possible, but also survivable. Hard fork risks are another reason it's good for the cryptocurrency economy as a whole to have viable alt-coins as options.