Is there any free (or free-ish) software available that allows me to burn stuff to DVD slightly more reliably than Windows Media Player?
Anything can be free if you put your mind to it.
That said, Nero :?
My trial period expired with Nero and I don’t know where I’d go to get around that.
Depends on what you’re burning to DVD…(Music? Games? Files?)
Nero’s decent. There’s also ImgBurn, Alcohol, and RealPlayer (should you try it).
Also, what Cless said: Anything can be free if you put your mind to it. 
That’s perfect! Thanks.