Up until this point, I have primarily focused on a particular interpretation of Genesis 1, called the "day-age" view, espoused by an organization called Reasons to Believe. However, I don't think their point of view is the full story.
First, it is clear that the divine workweek, while perhaps not 144 hours as we would understand a six-day period to be, is at least analogous to our workweek. Six days of work, one day of Sabbath-rest (see Hebrews 4). Some have used this as an argument for a 24-hour day interpretation. However, besides a human work week, other things follow this pattern of six "somethings" of work, followed by one "something" of rest. For example, Exodus 23 instructs us to work the land for six years, and for the seventh let the land "rest". This pattern itself actually follows work six/rest one-Sabbath pattern: a "Sabbath of Sabbaths" shall occur every fifty years, in the year of Jubilee (see Lev 25)! In other words, perhaps God created in this particular pattern in order to provide us with analogy to our prescribed pattern. This is called the "analogical day view", and provides one answer to the question as to why God did not just create everything in a big "poof". (Delving deeply into this may be a topic for later discussion.)
Second, it is clear that Genesis 1 should be interpreted within a literary framework. The framework hypothesis, if I am portraying it correctly, states that each of the days should be taken as part of a literary whole. Note the parallelism in the passage. In the first three days, God creates "kingdoms". Day 1: day and night. Day 2: the waters and the sky. Day 3: the land. Then, in the next three days, God creates things to fill these kingdoms (the "rulers"). Day 4: sun and moon. Day 5: swarming creatures in the ocean, great big ocean beasts, and birds. Day 6: specialized land-dwelling creatures, and, of course, humans.
Taking these two positions together, in addition to what I've already described, answers a couple outstanding questions. Why does the text appear to say that God created the sun and moon on Day 4? Not only is that because they are first clearly seen on Day 4, but also because it fits the divinely-orchestrated creation psalm that we call Genesis 1. Why does God seem to create sea-dwelling mammals (Day 5) before land mammals (Day 6)? Because Genesis 1 is not telling the whole story, only the essential points, and doing it this way fits the literary framework. Perhaps God did create land mammals on Day 5 as well. But the specialized ones, such as horses, goats, etc, important for human culture, perhaps were created on Day 6. These are the ones that are highlighted. One many also ask why He created in this pattern at all? Because of the importance of analogy to our workweek.
Wow. I really must apologize for the long time it took to finish writing this. I hope it was clear. But hey, one of the reasons why I'm writing this thing is to hopefully stimulate some discussion among friends and brothers and sisters in Christ. I'd really appreciate hearing what you have to say.