How can I recursively copy all pdf files in a directory (and it's subdirectories) into a single output directory?

  find /bunchopdfs -name "*.pdf" -exec mv {} /papers \;    

Here's a test I did

$ ls -R
.:
a  aaa bbb.pdf  pdfs

./a:
foo.pdf

./pdfs:

Notice the file "aaa bbb.pdf".

$ find . -name "*pdf" -exec mv {} pdfs \;
$ ls -R
.:
a  pdfs

./a:

./pdfs:
aaa bbb.pdf  foo.pdf

If you use bash in a recent version, you can profit from the globstar option:

shopt -s globstar
mv **/*.pdf papers/

find -print0 /directory/with/pdfs -iname "*.pdf" | xargs -0 mv -t /papers

(similar to another answer but I prefer pipe/xargs/mv ... more intuitive for me)

FYI, I did the above one-line script successfully on multiple directories and multiple pdf files.

For the Windows command line (cmd.exe), you can use:

for /F "usebackq delims==" %j IN (`dir /s /b *.pdf`) do copy "%j" c:\target_dir

If you're only searching one directory deep, you could do:

mkdir <destination>
mv */*.pdf <destination>

where <destination> stands for some directory. mv will not automatically create a directory for you.