The controlling reference for your question is Regulation (EC) No 562/2006 of the European Parliament and of the Council of 15 March 2006 establishing a Community Code on the rules governing the movement of persons across borders found here http://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX:32006R0562
One of the objectives of that regulation was to normalize all the various residence permits issued by all of the member states. It was initially given in Article 2 (15).
The list of residence documents given in Article 2(15) gets updated periodically, and the a recent update can be found at Update of the list of residence permits... here http://eur-lex.europa.eu/legal-content/EN/TXT/?qid=1418233047159&uri=CELEX:52011XC0708(04)
The section dealing with Romania lists 9 different types of residence permits issued by Romania, and you should consult this list to see if your residence permit is included. Your question specified only '
residence permit', so that's the extent of what can be given in this answer.
As part of an open consultation between Schengen members, some states have also improvised schemes allowing broader movement of Romanian residence permit holders.