Sunshine is a free application which shares files by transferring them directly from device to device. There's no lengthy upload/ download involved so it's quicker, and you don't have to be worried about who else might have access to your data because the transfer is encrypted and it's never stored anywhere else.
The program is available for Windows, Mac, Android and iOS, and you're able to transfer from any supported device to any other. Create an account via the Android or iOS app - just the usual "email, password" - or log in via Facebook and you're ready to go.
Select the media type you'd like to send, the individual files, and you're able to share them with your own local logged-in devices, Sunshine friends (others using the app), or by generating a link which you can send to anyone else.
It's also possible to stream media directly to DLNA devices on the same network, for example a smart TV.
The Sunshine interface isn't ideal but it worked without issue for us, and as we write it gets a good rating at both Google Play and the App Store.
Sunshine could be easier to use, and Google Play reviews suggest there are problems with some Android devices. It still has a four star rating, though, and we had no issues, so if you need this kind of direct transfer tool then it's worth a look.