find and remove files bigger than a specific size and type

find -type f \( -name "*zip" -o -name "*tar" -o -name "*gz" \) -size +1M -delete

the \( \) construct allows to group different filename patterns
by using -delete option, we can avoid piping and troubles with xargs See this, this and this
./ or . is optional when using find command for current directory

Edit: As Eric Renouf notes, if your version of find doesn't support the -delete option, use the -exec option

find -type f \( -name "*zip" -o -name "*tar" -o -name "*gz" \) -size +1M -exec rm {} +

where all the files filtered by find command is passed to rm command

If you want to exclude files by name, you can use this syntax:

find . -type f ! -name '*.mp3' ! -name '*.mp4' -size +1M -delete

or if your find does not support delete:

find . -type f ! -name '*.mp3' ! -name '*.mp4' -size +1M -exec rm {} \;

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