The short answer is: no, you should not. Not automatically, anyway.
The long(er) answer is that google does such a horrible job of translating texts that the text is either hard to read or simply doesn't mean the same as the original.
Dutch: "Mijn vlakbank kan niet van dikte zagen"
Actual meaning: "my planing bench cannot cut a board to the correct thickness"
Google: "My bank can not just cutting thickness."
Dutch:"Ik gebruik een schep om te scheppen."
Actual meaning: "I use a schovel for schoveling"
Google: "I use a shovel to create."
Dutch: "Vertel nog eens een moppie."
Actual meaning: "Tell me another joke"
Google: "Tell me a baby."
Dutch: "Deze grijze trui is mooi wollig, zit lekker en staat heel ruig voor op de kop af dertien euro."
Actual meaning: "This gray sweater is beautifully woolly, comfortable to wear and makes you look real rough, for exactly thirteen euros."
Google: (and I'm not making this up) "This gray sweater is nice woolly, is delicious and is very rough on the nose for thirteen euros."
Dutch: "Bing is beter than google."
Actual meaning: "Bing is better than google"
Google: "Is Bing better than google." (it's subtle, but the meaning goes from a statement to a question)
For those of you who say that "any translation is better than no translation", think again.
Firstly, when visitors read a series of texts in very poor grammer and spelling they will move on. Nothing gives the impression of amateurism and ineptitude more than a text full of grammer and spelling mistakes.
Secondly, the translated texts simply don't mean the same as the original. And they will be indexed by the searchengines and you will be ranked under keywords that have absolutely nothing to do with your site at all. Your website about gardening equipment is never going to be found in Dutch if every word related to "shoveling" is being translated as "creating" instead, and nobody is going to buy a sweater that is "delicious and rough on the nose".
So no, don't automatically translate your content through google. If you want to offer the translations as an extra service, create a button that opens a popup with google-translate in it, so the visitor can see that it's google thats making the mistakes and not you.