(Spoilers Extended) Jon Snow's Bloodlines

When assuming R+L=J we can trace Jon's lineage all the way back to [Aenar Targaryen].(http://awoiaf.westeros.org/index.php/House_Targaryen#Targaryen_Family_Tree) I must state that I've taken this information from the wiki (although most of the notes refer to The World of Ice and Fire), in addition I might have overlooked an ancestor or two, so take my answer with a grain of salt.

When tracing the lineage back to Aenar Targaryen, Jon Snow's paternal lineage includes blood ties to the houses: Targaryen, Blackwood, Dayne, Martell, Rogare of Lys, Arryn, Velaryon, and Baratheon.

The maternal Stark lineage is a bit harder to completely answer since their lineage stretches back thousands of years, therefore likely including houses which have long gone extinct or are not listed on the known family tree. Anyway, as far as I see Lyanna Stark's known lineage includes blood ties to houses: Stark, Locke, Blackwood, Karstark, Royce, Flint and Glover. With house Stark there is also the matter of Brandon Stark, the daughterless, and the wildling Bael the Bard .

/r/asoiaf Thread