Maybe.
We still don't know what conditions are necessary for life to form, or if what may form there could be considered 'life'. Nebulae have been shown to contain water, complex organic molecules, sugars, and other compounds important to life, but we don't yet know if life could arise there.
Most likely, only the very densest sections of nebulae could support life. The air we breathe has about 10^19 molecules per cubic centimeter; the densest discovered nebulae have only about 10^7 molecules per cubic centimeter. Most nebulae are far looser than that, ranging from 10 to 10^5 molecules per cubic centimeter. Only the most dense could even hope to support life, though even then it would be under vacuum conditions.
Perhaps some form of 'skimmer' life form, a huge living sail moving through the thin gas by pushing against it, siphoning up the gases and compounds it can metabolize. We don't really know, and I'm just speculating, but perhaps life could form in some distant nebula; however, it is unlikely that humans would ever find it, much less recognize it as living.
Another problem is that of scale: looking at pictures of nebulae, we fail to realize that they are clouds of gas and dust and vapor several TRILLION times the volume of our entire solar system. In that sheer mass, life may arise, evolve, and go extinct thousands or millions of times without anyone ever finding it. Habitable planets are needles in the cosmic haystack, but finding life-supporting nebulae may be like finding the a single specific water molecule out of all the oceans on Earth. Or life may be abundant in thousands of forms in every nebula in the universe. We don't know.
Long story short, life may exist in nebulae, but it's about a ten-trillion to one chance of us ever finding it until we have warp drive; Then it's just a hundred billion to one.
Triffid Nebula, Eagle Nebula, Cat's Eye nebula
A nebula contains stars and other matter; a supernova is just a large enough nova, or star that explodes at the end of its life cycle due to spent fuel
Low mass
Nebula are formed when a star explodes, releasing its gas into a gas cloud (the nebula). the nebula then will eventually condense due to gravity and form another star.
Emission nebula glow and reflection nebula reflect the light form other stars
A nebula may condense and ignite to become a star, conversely a star may explode and form a nebula.
In the nebula!
stellar nebula
The Boomerang Nebula is a planetary nebula [See related question]. It would have been formed when a medium sized star came to the end of it's life and in that process shed off layers of material from the star. This created the nebula we see today.
The Crab Nebula is a nebula.
None at all/ The life cycle of a star is based on it's initial mass, not where it was formed.
Triffid Nebula, Eagle Nebula, Cat's Eye nebula
A solar nebula is related to the formation of our Solar System, any other nebula is just a nebula.
nebula
Nebulas are interstellar clouds made of dust and gases and a pulsar is a kind of star. A pulsar is formed inside of a nebula, therefore a scientist could conclude that without a nebula a pulsar could not exist.
The Stingray Nebula (Hen 3-1357) is a planetary nebula. (The youngest known).
A nebula contains stars and other matter; a supernova is just a large enough nova, or star that explodes at the end of its life cycle due to spent fuel