0.0001BTC //now
0.00001BTC //soon
Agreed. For each node if a tx has insufficient fee (unless it is high priority) then it is dropped. It isn't included in the memory pool and it isn't relayed. Miners select txs for the next block by pulling from their local memory pool. If your tx isn't in that pool then you have no chance of being included in the block. For all intents and purposes your tx doesn't exist. Now some may ask why isn't it lower why not just allow tx w/ 1 satoshi fee and miners can decide if they want to include it or not. The problem isn't inclusion in a block, the problem is relaying. If lets say no miner will accept a tx w/ a fee less than 100 satoshis and all nodes will relay all txs regardless of the fee amount (or even 0 fee) then you could kill the network very easily by just flooding the network with tx that have a very low priority of ever getting in a block but it would degrade the performance of the network. Imagine if your (and everyone elses) node resource requirements increased by 1000x because someone was continually rebroadcasting 1,000,000+ txs which have almost no chance of being included in the memory pool.
Well there are two factors to be considered:
a) will a tx will be relayed and even kept in the memory pool of the miner
b) how long will it take for the tx to end up at the top of the memory pool and be included in the next block.
The first is easier to answer and understand. If your tx is low priority (less than 1 bitcoin day in age) and you do not include a fee equal to the min fee to relay, or any of the outputs are less than 5,430 satoshis (the dust threshold) then it is probably never* going to be confirmed. Most miners will never even see it. It is very likely that all your direct peers are running rules similar to the bitcoin-core and will just drop the tx. In essence nobody will ever see it. Now your node won't give up and it will keep rebroadcasting it and it will keep getting dropped. It can't be included in a block if nobody even knows about it.
On the second this is much more dynamic. It depends not only on your priority (or fee for paying txs) but the current and future priority (or fees) of other transactions. Miners will simply sort the txs. First they sort all the high priority txs by priority and include as many of them as will fit into the space reserve for free txs. Then they sort all txs by fee per KB and include as many of them as will fit into the total block size. All these parameters (min fee, kb of free txs, kb of total block space) are set by the miner. As a rule of thumb if your tx is high priority (even 57,600,000 exactly), under 1KB, and has no dust outputs then it will be relayed by all nodes. It will end up in the memory pool of all miners and it will eventually be included in a block. It might by luck by the next block or it might be one of the next hundred blocks but it will be included. It looks like most high priority txs make it into a block within a day.
* In theory eventually the rules might change such that the tx meets the new relay requirement or it might end up becoming high priority due to age and when either of those happen (assuming your nodes is still rebroadcasting) it will be relayed. Of course that could be months, years, or potentially never in your lifetime so as a practical matter I just say "never".
The min fee to relay is really just a DDOS prevention mechanism and thus is has been lowered five times since the genesis block due to the rising value of one Bitcoin. The fee has generally been lowered once it exceeded more than a few US cents and reduced to a fraction of a cent. The goal is to keep the min fee low but not so low as to make it possible to flood the network with no or little cost. As pointed out it is a crude system and in time will be replaced with floating fees but that is a more complex situation. In the interim it would be good if the min fee was less than what miners required to include txs in a block. This would mean the min fee isn't setting the "cost" of getting into a block, miners are.