I've heard the Chinese are fine to use the English word DVD, rather than the chinese word. What is more common, and what measure word do they use with it?
I had always used guanng pan (光盘) with ge (个), however I am told that it would be better to use pan (盘) or zhang (张). DVD is commonly used as is die pian (碟片) with the measure word bu (部) or zhang (张).
According to my Chinese friend DVD is most commonly used.
You will also hear wu（五 or jiu（九）after DVD if you're in a shop to signify the type of DVD (DVD 5 or DVD 9).
Just a supplement here. Many technical acronyms are borrowed directly from English, and we don't usually translate them into Chinese characters.Take DVD for example, its definition in Chinese is "数字多功能光盘“ as in English "Digital Versatile Disc", however, we don't say "数字多功能光盘", except that you want to explain what it is to other people.In general, we just say "DVD" and read it just in a letter-by-lettter way(Dee-Vee-Dee in this case). I would say "张" as the measure word for a piece of DVD. Some other examples:
LED (read: el-ee-dee)
LCD (read: el-see-dee)
Mp3(read: em-pee-sān) We use this word to mean a file with .mp3 extension or a mp3 player.
Jpeg(read: jay-pee-ee-jee. I have heard an American read it as "jay-peg", but I have never heard my chinese friends read that way)
My old textbook  claims that 看碟 is used to say watch a movie on DVD.
Yellow bridge  says 影碟 is used for DVD, and its measure word can be either 张 or 片.
 Integrated Chinese 3e, Level 1 Part 2, Lesson 11, p2
I don't know that I've ever heard a Chinese person say anything but DVD to describe a DVD, although I remember learning 光盘/数字光盘 (guāng pán/shù zì guāng pán) as CD/DVD when I was doing my Chinese course.
The measure word for DVD is either 盘 or 张 - either one is fine so far as I know, although a native speaker might correct me on this.