I've sent some BTC with a low fee..
0.0000001 is not a low fee, it is an invalid fee that will cause your transaction to be immediately discarded by any nodes or miners receiving it. You will need to remove the record of this transaction being sent from your own wallet to restore the balance shown to you, and then switch to a wallet that doesn't let you do silly things.
Hm, what's the criteria for validity?
It doesn't look discarded as blockchain.info sees it. Anyway, how do I remove the record of this transaction from wallet?
The wallet I'm using is bitcoind.
Either send with 0 fee or the standard fee, anything in between seems only to delay your transaction significantly.
That is not true. The user's low fee is treated as zero by miners so it is pointless but it doesn't make it worse than 0 fee. There is no point in paying a fee less than 0.1 mBTC because the code used by miners to prioritize txs treats those as free. So 0 BTC or 9,999 Satoshis or 1 Satoshi are in the exact same category.
The issue is there is a massive backlog of free txs. User deleting the tx and paying no fee puts him in the same situation.
So either:
a) delete the existing tx and create a new one which pays a fee of 0.1 mBTC (or higher but that really isn't necessary).
b) simply wait the tx will eventually confirm (could be hours more, days more, maybe weeks more).
Free tx should be considered charity. Anything below the 0.1 mBTC threshold is considered free by miners.