I've heard conflicting reports of how the creation days , יוֹם (yowm), in Bereshit are interpreted in the Jewish community. How do actual Hebrew scholars define day in Bereshit? six 24 hour periods or six long periods of time? Is one view favored over another(By hebrew scholars), does each viewpoint have about equal support, or is there no argument?
Short answer: There are different opinions, each with their own proofs and backings.
Long answer: Avi's answer explains the different meanings of "yom" quite well. It is my understanding that up until recently, most Rabbis agreed that in regard to creation, it meant a 24 hour period. Once scientists came up with theories about the age of the universe many Rabbis began to engage in what has been called "apologetics", explaining that "day" was metaphorical for "eras".
In my experience, whenever something in the Torah isn't meant literally, its always explained in the Talmud. The most famous example of something not meant literally is "an eye for an eye" which the Talmud says quite clearly (Bava Kamma, 83b-84a) that it refers to monetary compensation. There is no such explanation in the Talmud regarding "day" in Bereishis.
You asked for personal opinions so I'll say that I firmly believe that it was 24 hour periods. If it had meant anything else, certainly that would have been part of the oral tradition. Instead, the Rabbis in the Talmud explain what happened in each hour of the sixth day (Sanhedrin 38b). In addition, if it hadn't meant "days" literally, the Jewish observance of Shabbos as the seventh day of the week would be pretty meaningless. In fact, the entire concept of a seven day week would have no point. Also, the addition of "it was evening and it was morning, the _ day" makes it quite clear to me that it was a "day" in the traditional meaning, albeit without the sun.
As a final point, the Lubavitcher Rebbe points out in a letter that there are those Rabbis who don't hold that the six days are literal, and therefore say that the world is older than 5771 years (as of this writing). For these Rabbis there is a serious problem with the text of the "get" or bill of divorce. Halacha is very stringent with the exact text of the bill (here and here), because if the intended meaning is changed slightly - the bill is invalidated, the divorce is not valid, and any remarriage becomes adultery. On the bill of divorce, there must be written a date, and this date must be of the form - "Five thousand seven hundred and seventy one years according to the creation of the world according to our counting here". The Lubavitcher Rebbe points out that this would be contradicted by any interpretation of "days" being "epochs" or "eras".
In Genesis 1:5, yom obviously means a regular day. Evening and morning is used, as well as a number.
Now if you look at Exodus 20:9-10 it says "6 days you shall labor and do all your work, but the seventh day is a Sabbath to Yhwh your God". Now yom here obviously means a regular, 24-hour day. But if you read on we'll see the reason for the Sabbath.
In Exodus 20:11 it says "For in six days Yhwh made the heavens and the earth, the sea, and all that is in them, but he rested on the seventh day. Therefore Yhwh blessed the Sabbath day and made it holy". Now the Sabbath would be meaningless if it was based on 6 indefinite time periods.
And also, this solves the problem with the "indefinite" period between Genesis 1:1,2 and Genesis 3. It says, "For in six days Yhwh made the heavens and the earth, the sea, and all that is in them". Plus, it says Yhwh created everything, therefore verifying that Genesis 1 and 2 are about the same creation.
When you look at the Hebrew bereshit, the first two words in Genesis, most translations say "in the beginning", but actually it means "in the beginning/start of". So if you literally translate the first verse in the Bible from Hebrew, it reads "In the beginning/start of God create the heavens and the earth," Now the Hebrew word for create is bara. You can't tell if it's past, present, or future. English versions always put it in the past tense, but a lot of Hebrew scholars think it is in the present. So therefore it would read, "in the beginning of God's creating of the heavens and the earth",
This makes much more sense, and it agrees with Exodus 20:21. And in Hebrew, Genesis 1:2 is clearly a description of when God was creating in Genesis 1:1. So the first two verses of Genesis should be, "In the beginning of God's creating of the heavens and the earth, when the earth was without form and void..."
This means that the universe is only around 6,000 years old.
The 'catch all' meaning of the word 'yom' is 'time period'
The precise meaning of yom in tanach has 4 meanings depending on the context.
In Bereshit(Genesis) both the first and second meanings of the word are clearly used and the 4th meaning of the word is arguably used. There is no single opinion agreed upon by everyone as to which meaning is used where.
It is agreed upon by everyone that the word 'Yom' is not used to mean the rising and setting of the sun however, because the sun was not placed in the sky to rise or set until the 4th yom. (though 24 halachic hours is still the pshat, it's just not sun related halachic hours) And the Yom that is light, is defined in the first day. This often leads to understandings that the light of the yom is a spiritual rather than physical light. (see Rashi)
The idea of a yom in bereshit being a very long period of time comes from tehilim, where it is written 'A day in your eyes is like one thousand years'. This then question's as to who's perspective the creation story is told before Adam is created.