It may seem obvious that we should 'look after' the world that Hashem gives us but is it considered a mitzvah to involve oneself in nature conservation and/or recycling?
As mentioned in NBZ's answer, the Torah prohibits destroying fruit trees, and this prohibition extends to destructive and wasteful behavior in general (Rambam, Hil. M'lachim 6:10).
Additionally, we are encouraged to maintain our surroundings properly. Rashi (Bava Kamma 6a, s.v. Biymos hachamma) explains that it is forbidden to empty to one's drains and gutters into a clean street since it will make it dirty (see also Shulchan Aruch CM 414).
In the Talmud's (Shabbos 33b) illustration, when our forefather Ya'akov arrived in Shechem, he established a local currency, constructed public roads, and built public bathhouses. As Rashi (B'reishis 33:18-20) points out, when Yaakov encamped in this new locale, he also enhanced it (the Hebrew words for "encamp" and "beautify" share the same root); when he purchased land, he also improved it ("purchase" and "improve" share the same root in Hebrew).
So it appears that we should maintain our environment and certainly not destroy it. Whether these considerations affect conservation of uninhabited areas or require recycling is less certain, and I'll leave that for another poster to address.
We are obligated in passive nature preservation of natural valuable resources. Those of no value are possibly included too. When the author of the following tshuva* was asked about an active obligation, he responded that he doesn't know a source for such a mitzvah. (Emphasis is mine.)
one who Breaks dishes or tears Garments or destroys anything of value is violating the Prohibition in the Torah called Baal Tashchis.
The shita of the Rambam in the Laws of kings chapt 6 hal # 5 As per the Teshuvos chasam sofer choshen mishpat 27 is that It is a torah prohibition.
The Noda beyehuda disagrees in His responsa Yoreh deah # 10 and considers it a rabbinic Prohibition.
Agreeing with the Noda Beyehuda are great poskim such As the responsa Mahari bessin, Mishne lemelech,responsa of Beis Yitzchok #142 ,the Chaye Adam in hilchos tzitzis.
The prohibition against being Wasteful is even if the object being wasted is from Hefker according to the above mentioned teshuvos noda beyehuda and The Baal hatanya In his shulchan aruch Harav hilchos shmiras haguf.
There is an unresolved discussion regarding wasting an Object that has no monetary value.
The teshuvos hisorres teshuva vol2 # 183 and teshuvos chavalim banimim. And Rav Yosef C Sonnenfeld ,zt'l Remain with this doubt.
spending money mindlessly is Included in the Prohibition of Baal Tashchis according to Rabbenu Yonah in Shaarei Teshuva 3-fn 82 and semak mitzva # 173
* R' Leib Tropper's e-mail list, Shoel and Meishiv, May 23, '13.
To add to the previous answers, I would say that there isn't really much in ironclad halakha about recycling for obvious reasons and to get a "Jewish View" we'd have to go back to Tanach where things are ambiguous as usual. On the one hand one can quote "לעבדה ולשמרה" (Genesis 2:15) as evidence that that conserving nature is man's sole purpose. On the other hand, we have several verses such as Genesis 1:28 and Isaiah 45:28 indicating that it is mankind's place to use nature in service of man (ultimately in service of God but that's a separate issue) in which case conservation is only a "Jewish Value" insofar as it's common sense to keep natural resources around to use.
This is a relevant Q&A from Rav Aviner's website although there are no sources:
Q: Is Halachah "Green", obligating us to be concerned about environmental issues? A: Yes. It is forbidden to cause damage to the environment. But we must always weigh the expense of protecting it against other essential expenses such as food for the poor, education and the military.
The Ramban in parshas Ki Seitzei chapter 22 vs 6 mentions a second reason for shiluach hakan and not slaughtering the animal with it's child on the same day which seems pertinent to the question at hand. 'The reason for both (commandments) is so we shouldn't have a stern heart and not have pity. Or so that scripture should not allow a complete destruction, to uproot a species. Even though it allowed the slaughtering within that species. But if someone were to kill the mother and child on the same day, or take them before they have a chance to fly, its as if he perpetrated an extinction of the species.' What we see is we may use, not abuse or use up.