Are there any miners that will always include microtransactions even when no fee is paid?
Yes.  All miners using the default Bitcoin Core settings will include some free transactions in their blocks based on priority.

Let's say you have a microtransaction-sized 5,000 satoshi input (about $0.01 USD presently).  According to Bitcoin Core 0.10.0's estimatepriority RPC, you currently need 59985719 priority to get a zero-fee transaction mined within 25 blocks (~4 hours).  That means you'll only have to wait until your input is about 46 years old:

satoshis * blocks per year * years / tx size &gt; priority
5000     * 52596           * 46    / 200     &gt; 59985719


That's because priority is computed by input amount in satoshis, times the number of blocks since it was received, divided by the number of bytes in the transaction.

I haven't heard of any miners that have free transaction policies that are more generous than the Bitcoin Core defaults.