Can systems that prevent double-spending (e.g. crypto-currencies) be used to attach other unique data?
In theory, yes, a peer-to-peer validation network could be used to enforce any unique content (not just money) assuming a sufficiently large validation network.

"Sufficiently large" is the catch. Bitcoin validates transactions by having the network nodes "vote" on the transaction's validity. According to Satoshi's proposal: 


  The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes.


Getting enough honest nodes into your validation network that no amount of compromised or attacker nodes can affect validation would be very hard. You would also probably want these nodes to be controlled by a large number of people. With a large number of nodes and a small number of controllers, it would be easier to compromise significant portions of the network and it would also reduce trust in the network since, despite the number of nodes, the control is still only in the hands of a few. Bitcoin (and all of the other cryptocurrencies that I am familiar with, which admittedly, isn't a lot) accomplished this by incentivizing its validators; Bitcoins are periodically awarded to the "miners" who solve the proof of work problems in the transactions. This also happens to be a convenient way to introduce new Bitcoins.

However, this would be particularly difficult for the digital trading card scenario you mentioned, since that kind of service would likely only appeal to a niche audience. Even if you incentivized by awarding cards, there might not be enough individuals interested in operating validation nodes.

A scheme where a central authority issues the money (or other content) might not fare much better, since, in practice, the central authority would probably either end up controlling or having material influence over a large portion of the network. Remember that the Bitcoin network issues coins, not the Bitcoin devs or any other single person or small group of people.

The take-home is that if you can get enough people to participate in the validation network, then you should be able to defend the uniqueness of any information (money isn't special in this regard). However, getting enough people to participate would probably be incredibly difficult.