Edit, 28.06.2016
There is a Background on PlotMarkers on 10.0 for Mac OS X x86 (64-bit) (December 4, 2014) with the StandardReport style:
bgc = White;
ListPlot[{{1, 1}, {2, 2}}, Background -> bgc,
TicksStyle -> {{12, Background -> bgc}, {12, Background -> bgc}},
Joined -> True, PlotMarkers -> Automatic]


There is no Background on PlotMarkers on 10.0 for Mac OS X x86 (64-bit) (December 4, 2014) with the StandardReport style when using BaseStyle -> {Background -> None}:
bgc = White;
ListPlot[{{1, 1}, {2, 2}}
, Background -> bgc
, TicksStyle -> {{12, Background -> bgc}, {12, Background -> bgc}}
, Joined -> True, PlotMarkers -> {{Graphics[{Disk[]}], 1/4}}
, PlotRange -> {{0, 3}, {0, 3}}
, BaseStyle -> {Background -> None}]


There is no Background on PlotMarkers on 10.0 for Mac OS X x86 (64-bit) (December 4, 2014) without the StandardReport style.
bgc = White;
ListPlot[{{1, 1}, {2, 2}}, Background -> bgc,
TicksStyle -> {{12, Background -> bgc}, {12, Background -> bgc}},
Joined -> True, PlotMarkers -> Automatic]

And the the marker size can be tuned like so (see How can I change the size of the plot markers):
ListPlot[{{1, 1}, {2, 2}}
, Joined -> True
, PlotMarkers -> {{Graphics[{Disk[]}], 1/4}}
, PlotRange -> {{0, 3}, {0, 3}}]

PlotMarkers -> Automaticand transparent background withPlotMarkers -> None. It works for me (Linux, V10.0.1) but contradicts the docs, which sayNone= no markers. – ybeltukov Jan 28 '15 at 18:56PlotMarkers -> {}– Jan 28 '15 at 20:18PlotMarkerson my plot (Mac OSX, v. 10.0.0). – David G. Stork Jan 28 '15 at 21:05