The Dropbox Ubuntu package almost works on Debian Squeeze … except for one dependency with a numbering scheme that differs between Ubuntu and Debian.  Here is a quick script that extracts the package, corrects the one dependency in DEBIAN/control, and repackages, leaving a new .deb suitable for Squeeze.

convertDropbox4Squeeze:

#!/bin/sh
if [ $# -ne 1 ]; then
	echo "Usage: $0" 'nautilus-dropbox_$version_$arch.deb'
	exit 1
fi
DIR=`mktemp --directory`
mkdir -p $DIR/DEBIAN
dpkg-deb -x $1 $DIR/
dpkg-deb -e $1 $DIR/DEBIAN/
sed -i s/'libnautilus-extension1 (>= 1:2.22.2)'/'libnautilus-extension1 (>= 2.22.2)'/ ${DIR}/DEBIAN/control
dpkg-deb -b $DIR  ${1%.*}_squeeze.deb
rm -rf $DIR

Just download the .deb from the Dropbox site, then run

./convertDropbox4Squeeze nautilus_dropbox.......deb

And then just install the newly created nautilus_dropbx….squeeze.deb .