About travel your residence card should liberate you from the visa requirement in all EU-countries. However please be adviced, that Great Britain and Ireland do at present not follow these rules, even though they should. So if you plan to visit one of these 2 countries, you will either need to apply for a visa regardless of the rules or spend several years bringing the case to court, before you can make your trip without a visa.
And unless you are, what in danish is called a "principrytter", obviously the far easier solution is to just obtain the visa. Or even better punish these countries financially by not going there at all and consequently spending your money and generate a tax revenue somewhere else.