Haven't had much trouble with SVT Play. The minor headaches that I've had have been with videos that aren't allowed to be viewed outside of Sweden. Just haven't saved them.
I hear it could be possible to also get those but I've never bothered to check.
I also think that their player pages are truly user-friendly because they provide 'a link for an external player' (one just has to disable Flash to see the link (or look at the page source within a browser and search for 'external-player' to find the URL)). With that it's usually easy to download stuff.
Programs I use for saving (from SVT Play) are
MPlayer (for http URLs) (could be done with
VLC Media Player too) and
RTMPDump (for rtmp URLs). I also occasionally use
webvi command line client (for Linux only as far as I know
).
I think there could be many other players or downloaders that can do the work. Just never bothered to search ('cause things have worked for me)...
And yes, all the programs I mentioned are
free.