Bitcoin has had two significant reorgs of greater than 6 blocks in the past.
The value overflow incident in 2010 was the result of a bug which created 184 billion bitcoin. Satoshi patched it in around 5 hours, everyone moved to the new patched client, and 53 blocks were ultimately made stale.
The release of v0.8 in 2013 also caused a fork due to a block being mined which was incompatible with v0.7. It was ultimately resolved by users downgrading back to v0.7, and resulted in 24 blocks being made stale.
Outside of these bugs, the longest reorg I am aware of is 4 blocks, starting at block 174,161.
2015 SPV mining fork had quite a long fork as well, 3 and 6 on the two occasions. You'll be affected with either a SPV client or an old Bitcoin Core version. Neither of which can validate BIP66 enforcement. Granted this only affects those two kinds of client which are unable to validate and relies on the longest valid chain.