... umm for science
But in all seriousness, I attempted to send some trivial amount (.1 mBTC) without a fee from the Android wallet app and the transaction has been hanging in limbo for the better part of a week, leaving a few bitcents that I can't use. My understanding is that the only way to use those coins is to a) wait an indeterminate amount of time until that transaction gets accepted or b) double spend that "chunk" to myself with a fee to get it into the block chain in short order.
From the Bitcoin Android wallet app? or from Blockchain.info for Android? or something else?
That's a long time for a transaction to hang out there without getting a confirmation. The original sender must be re-broadcasting it periodically (which is what the client is supposed to do).
But because it has an output below 0.01 BTC and it has no fee, not all nodes are relaying it. So you still might be able to spew out a double spend that would get relayed.
So if you have the private key for the address from one of the inputs for that send transaction you can import that address into the Bitcoin-Qt client, or Multibit, or Electrum, etc. and try to spend from one of those. You'll have the same problem if the amount is below 0.01 BTC and you don't pay a fee though so make sure to pay the freight.
[Update: Just remember though, with Bitcoin-Qt if that is a failed double spend attempt there's no way to delete the offending transaction from the wallet (without using the third party tool, pywallet, to perform wallet surgery). So don't do this with your normal wallet.dat for Bitcoin-Qt, or at least make a backup right before so you can restore the old one if the double spend attempt never confirms.]