The current vitality of independent movements is greatly exaggerated. You cannot assume that opinion polls and speaking about independence are the same thing as actually trying to get independence. Gaining independence is hard.
There are a few countries, or regions, that are already de facto independent such as Transnistria or Kosovo, but do not have official recognition.
There are a few regions that have historically tried to get independence, even with terrorism, but do not currently have a serious movement for independence, such as Corsica or South Tyrol.
There are a few regions that could probably create a serious independence movement, because they have strong regional identities and parties. These are regions such as Bavaria or Flanders. However, they are not currently doing that.
There are a few regions that have expressed the desire to get independence and actually done something about it:
- Basque Country. Although there has a been a move toward more autonomy instead of independence. For instance, the end of terrorism attacks.
- Scotland. They had a referendum and independence lost. Brexit might have caused some regrets and declarations by politicians, but nothing will happen in the next few years until Brexit is finalized.
- Northern Ireland. Just like the Basque ones, the Northern Ireland independentists have abandoned terrorism. They also moved toward autonomy. Independentists movements have not nominally abandoned the quest for independence from United Kingdom and reunification with Ireland, however they have not made real initiatives for it. Overall, it seems that the Good Friday Agreement has satisified most people. If Brexit is managed really horrendously they could reignite a movement for independence. Normally the chance would be very slim, but given the current track record of the Conservatives it may actually happen.
Finally, there is a region that is de facto independent, but is trying to get back with the rest of the country: Northern Cyprus.
 That is not to say that there are only two possibilities: terrorism/violent rebellion or autonomy. It just happened that both groups did the same things together. Thanks to @inappropriateCode for having pointed out the bad phrasing.
 Thanks to @pjc50 for having pointed this out.