I have been a heavy user of Amazon prime for years, and it baffles me why anyone shops offline for anything but perishable grocery items. If shopping is something you enjoy as a recreational pastime, you can stop reading now, but for all the rest of us, read on to see why Amazon Prime is not just good for your budget, time, or carbon footprint.
Let's start by making some assumptions. First, I will assume that you earn exactly the national median for a fully employed person in the US: $32,140 which is approximately $15/hour . I assume you spend money like a typical American as well, meaning that you spend approximately $7,423 per year on personal care, misc, alcohol and tobacco, apparel, and entertainment . I assume you have access to a car  that gets the national average of 24.1 mpg . Further, I'm going to assume that you are like 90% of Americans and live within 15 minutes of a Wal-Mart  which represents an 8 mile distance . I will make the further simplifying assumption that you purchase all your goods at Wal-Mart. You value your free time at $10/hr or a 2/3 of your working wage. Your primary shopping objective is to save money on the goods you want and need.
I will assume that most of your shopping is done for relatively common goods, which is just to say that you are not trying to find a new Tiffany diamond necklace, you're shopping for things like shoe laces, t-shirts, and garbage bags. I will assume you shop about as much as the average American, or .75 hours/day , and that a typical shopping trip requires 2.16 hours for a total of approximately 127 shopping trips per year.
The Cost of Offline Shopping
Let's start by calculating the costs associated with your current shopping habits. 127 shopping trips per year means your car is being driven 127 * 8 = 1016 miles per year getting you to and from the store. The IRS mileage rate is $.56/mi , which means you are spending $569 in car depreciation every year to shop. Further, at 24.1 mpg, and an expected fuel cost in 2013 of $2.04/gal (so cheap!) , you're spending $83 on gas for those trips. The total cost to you in terms of automotive expenses is therefore $652/year.
Then there's the time cost. Shopping takes time away from doing other enjoyable things, like watching movies, taking walks, and eating with friends. In the above assumptions, we put the cost of your time at approximately 2/3 of your working wage, $10/hr, which means that you are paying yourself 274 hours * 10 = $2,740 to go shopping. So far, the total cost of shopping offline is $3,392 per year and that doesn't count any of the unpleasantness of fighting through weekend traffic, having to visit multiple stores (because remember, in this hypothetical example you only ever have to shop at one store), and finding a parking spot at an already overcrowded mall.
The Cost of Shopping on Amazon Prime
With Prime, goods are delivered right to your door and the actual finding and purchasing of goods requires significantly less of your time. Consider a simple example to demonstrate the point: it would likely take you less than 15 minutes to find a common item like a serving ladle (not an affiliate link) on Amazon which is less than the one-way time required to get to a store. If you were able to avoid only 25% of your shopping runs over the course of the year, that would be 68.5 hours of your life back. We're talking about a 2.8 day's worth of time you can could spend playing fetch with your dog, socializing with friends, or reading interesting blog posts like this one. That's 8 days of vacation time from work. If you are aggressive about shopping online, you could easily avoid far more than 25% of your shopping trips.
Prime costs $79/year (soon to be $99), restricts buyer choice, and recent studies have shown that Amazon can cost as much as 20% more than Wal-Mart . But it's still a money saver. The average American is spending $7,423 on non-grocery non-medical purchases per year (see the CNN money link in the footnotes below). $7,423 * .2 = $1,484, add the $79 subscription fee, and it costs $1,563 more on average to shop on Amazon compared to Wal-Mart. If you shop at Target, Macys, or any other more expensive retailer, the cost savings is likely to be much smaller. Compared to the cost of offline shopping calculated above ($3,392), however, Amazon will save you approximately $1,829 ($3,392 - $1,563) per year in automotive upkeep, gas, and time.
In addition, the estimated 20% premium is an estimate based upon a relatively small sample size for non-Prime customers. So the above estimate is likely understates the actual savings.
Shrink Your Carbon Footprint
Finally, shopping online is better for the planet because it significantly reduces the energy cost of shipping goods to consumers . The most efficient way to deliver goods to end users is on big trucks, planes, and delivery vehicles like that UPS truck with all the Amazon packages in it. True, such trucks get poor mileage per gallon, but they deliver hundreds of packages per run, and unlike your personal vehicle, UPS and other shippers are spending big money on reducing their fleet mpg .
Amazon Prime saves time, money, and helps me be a reduce my carbon footprint. The $79 might sound like a lot, but it's a drop in the bucket compared to the improvements in quality of life. And if you are like me and dislike shopping in the first place, all of these calculations are meaningless. I would actually be willing to pay more to avoid the mall, but Prime has conveniently given me a better option. You can check it out here (non-affiliate link): http://www.amazon.com/gp/prime
 Personal income in the US: http://en.wikipedia.org/wiki/Personal_income_in_the_United_States
 This comes from the CNN money breakdown of American expenses: http://money.cnn.com/interactive/news/economy/us-spending/
 For every car in the US, there is 1.3 people, so this seems pretty reasonable. http://en.wikipedia.org/wiki/Motor_vehicle
 Presumably if it is newer, you'd be more likely to get good gas mileage, but I'm working with averages here. http://en.wikipedia.org/wiki/Fuel_efficiency
 It's actually pretty shocking that we all live so close to Wal-Marts, http://www.statisticbrain.com/wal-mart-company-statistics/
 This is an extrapolation from the statistic about living 15 minutes from a Wal-Mart. I do not have a statistical source to back up the conversion from 15 minutes to 8 miles, I'm just guessing you can't go 60 mph on the way to the average Wal-Mart from the average home.
 Yes, that means that the average American spends 274.13 hours shopping every year: http://www.bls.gov/news.release/pdf/atus.pdf
 2014 IRS mileage compensation rate: http://www.irs.gov/2014-Standard-Mileage-Rates-for-Business,-Medical-and-Moving-Announced
 Expected cost of gasoline: http://www.nytimes.com/2015/01/28/business/energy-environment/after-steadily-falling-price-for-gas-notches-an-increase.html
 The study was conducted by Kantar Retail. Their sample size is pitifully small (36 goods) and doesn't take into account the fact that Amazon doesn't cover all goods with Prime shipping: http://www.bloomberg.com/news/2012-06-22/wal-mart-beats-amazon-prices-including-glee-dvd-set.html
 The study is actually focused on Buy.com, which presumably has a less efficient distribution network than Amazon: http://campustechnology.com/articles/2009/03/16/shopping-online-more-energy-efficient-say-carnegie-mellon-researchers.aspx