Y-DNA evidence indicates that there are four unrelated major lines of Plummers, and several minor ones.
The Anne Arundel (Thomas) Plummers were Y-DNA haplotype G, probably G2a3b1 (rather rare, and suggestive of French - possibly Capetian? - ancestry somewhere back in the distant past). They were also very strongly committed Quakers, and most (but not all) of them stayed that way for generations, even after moving out of the area.
The Massachusetts (Francis) Plummers were R1b1a2 and absolutely no relation to the Anne Arundel group, despite the popular historical fiction that Francis and Thomas were "brothers".
The Kemp Plummer line, out of Virginia and North Carolina, was I2b2. (Here's a chatty letter from a woman of that family to another female relative: http://sparedandshared.wordpress.com/letters/1844-lucy-martin-plumm... )
There's a line out of Pennsylvania (Richard and Isaac Plummer) that 's the rather unusual R1a1a - more common in Eastern Europe and western Asia than in western Europe.
Minor lines include several more flavors of R1b1a2 (including one from Wexford, Ireland, of which at least one member went to Canada), a couple of J2s, an I1, and an I2a2b who may not have been a Plummer by birth (he is said to have been adopted).
More information is available here: http://www.worldfamilies.net/surnames/plummer (not all of their lines are accurate, so double-check carefully!).