there is a great plugin doing that, it is jvectormap :
it is very lightweight & cross browser (vml is used for non svg support) & very easily extensible (which imo is better than have a plugin full of option you don't need, here it has the minimum then you add what you need) through on click, on mouse over call back to start with & that shall be enough for most cases.
lightweight if you convert your map correctly (limit to the max the level of details). now the conversion of the vector map for use by the plugin can be tricky but there is a wiki about it :
https://github.com/datag/jvectormap/wiki/Map-converter-notes
i've redacted the part of the wiki about using GIS software on ubuntu. using SAGA-GIS was indeed a saviour & a good thing to learn to publish any map for the plugin in no time.
I'll add that i've tested anymap from anychart & fusionmap from fusioncharts and that imo jvector is the winner without any contest for cross-browser/customisation ease/flexibility/bandwidth/execution efficiency... & last but not least it is free !