To find and remove core files conditionally:
# find ~ -name core -exec file {} \; -exec rm -i {} \;
"file" will show which executable the core file is for and the -i option to rm will allow you to choose weather to delete it or not.
# find ~ -name core -exec file {} \; -exec rm -i {} \;
/my/home/core: ELF 32-bit LSB core file of 'netscape-commun'
(signal 3), Intel 8
rm: remove `/my/home/core'? y
Alternatively, if you just want to remove the core files without knowing what file generated them, the use the following
find ~ -name core -exec rm -f {} \;