I guess the official Dropbox is not out yet heres one that is, http://www.androidzoom.com/android_a...pbox_fiuk.html
plus DroidBox http://www.androlib.com/android.appl...-com-wwqt.aspx

plus there is a mobile version of DropIO called DroidDrop http://www.androlib.com/android.appl...drop-qAqC.aspx
I'm not sure where you can find the apk files online. It will require patience and searching. I have had luck emailing developers and they have sent me apk files in the past. That might work.
Also have you tried Skydrive (you get 25 GB of online storage free) or Live Mesh (only 5GB) - both accessible from a web browser.