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As long as your blue card is still valid, you can in any case visit other countries in the Schengen area (that's most of the EU together with a handful of other countries like Switzerland and Norway) for up to 90 days. You can also visit Romania, Bulgaria, Cyprus and Croatia (EU countries that are not Schengen members yet but apply the same rules).
Even though they are full EU members, the blue card, along with most other German residence permits does not grant you the right to visit the UK or Ireland. Depending on your citizenship, you might therefore need a visa to go there.
There are also a few non-EU countries that exempt some Schengen visa holders from the requirement to get a local visa (e.g. Serbia, Bosnia-Herzegovina) but I am not sure this exemption also covers residence permits. Depending on your citizenship, you might therefore need a visa to go there too.
Beyond that, I don't know whether your blue card would still be valid. My guess is that it might depend on how you left your job and other details of your circumstances but that's more of an expat than a travel question.