Seeking API to return GeoJSON data for countries borders?

If you do not find any it is not difficult to set up your own. Install Geoserver and you can get geojson out from WFS with requests like

http://demo.opengeo.org/geoserver/wfs?service=wfs&version=1.0.0&request=getfeature&typename=topp:states&outputformat=application/json&propertyname=STATE_NAME,the_geom&CQL_FILTER=STATE_NAME=%27Illinois%27

You just need to install world_boundaries shapefile into your server or save it into PostGIS database and you have a pretty rest-alike service for country borders.

ThePlacename.com has an api that returns place borders in GeoJSON format: http://theplacename.com/restapi