Questions are often asked if you hold a spouse/partner visa or biometric residence permit, can you travel through other EU countries without visa? Since most other EU countries are covered by Schengen visa, the reply only deals with it.
If you are a visa national for the Schengen countries, the fact that having a UK spouse visa doesn't exempt you from obtaining Schengen visa. Some non-Schengen countries like Ireland may have special rule for UK spouse visa holder, which you need to find out from the country in question. Often their embassy website in London carries details. So for example if you are an Indian national, hold UK spouse visa and want to visit France, you will require Schengen visa in advance - it can't be obtained at the French border, and without it you will be refused to board the flight or Eurostar to France. The fact you hold spouse visa does mean your application will be fast-tracked (at least in theory), you don't have to give details about booked accommodation etc (i.e. you don't need to answer questions on visa application form marked with *) and no fees are charged. Also you are more likely to be issued with a visa valid a year or more (but each stay is limited to 90 in 180 days) so you don't have to get a new visa for each trip.

If you are here under the EU regulations as a family member of non-UK EEA citizen, and you have residence card valid 5 years, then you don't need Schengen visa, provided you travel with your EEA partner or you are joining your partner at the destination. So if you are married to a German citizen and you hold residence card issued by Home Office, you can travel to Spain without Schengen visa with your partner. Such residence card is called Article 10 residence card. Also if you are in UK after utilising Surinder Singh provision and hold residence card, you can visit without Schengen visa. Remember, you must hold residence card and not just EEA family permit or certificate of application (COA), and you must travel with your partner or are reuniting with them. Otherwise you require Schengen visa.