With all due respect to Narzos, the author of the previous writeup, I really think one cannot determine the Earth's carrying capacity until one knows the Earth's Strength attribute.
A typical, human-sized Dungeons and Dragons character, going by the new Third Edition rules, and with an average Strength score of 10-12, can easily lift between 33 and 43 pounds of equipment. However, the full D&D 3rd Ed. Strength range goes all the way from a score of 1 (which can lift a mere three pounds – and please, don't ask for that in kilograms) to no maximum. The highest a generated human can have is 18, but the highest listed in the chart in the Player's Handbook is 29, and it supplies a rule-of-thumb chart continuation that suggests multiplying the total by 4 for every additional ten points of Strength.
The question has been made all the more difficult due to the changes since the previous editions of the game. In the First and Second editions all characters' and monsters' carrying were rated on the same Strength table, regardless of size. Now the size of the monster imparts an additional multiplier to the creature's carrying capacity. So a pixie, being of Small size, even if she somehow had a human's normal strength, can still only carry three-fourths as much as a human, or any other, medium-sized, creature of the same strength. (The somewhat more difficult calculations needed to figure out the carrying capacity of a planet are just about exactly offset by the long-overdue abolition of the Percentile Strength kludge-system, which I am surprised was even introduced in the first place.)
But in the interests of silencing the Earth carrying capacity debate once and for all, and returning Everything users to their important work, I will attempt to, once and for all, answer this burning question.
The weight of a Medium creature in D&D is between 60 and 500 pounds. Large creatures weigh between 500 and 4,000 lbs., Huge creatures from 4,000 to 32,000, Gargantuan from from 32,000 to 250,000, and Colossal from 250,000 lbs. up. However, the rate of increase of the upper limits to the weight from each size category to the next actually declines, from x12 from Medium to Large, x8 from Large to Huge, and 7.8125 from Huge to Gargantuan. According to the information contained at http://www.england-insight.com/maths1.htm, the weight of the Earth has been recalculated and is now thought to be 5,972,000,000,000,000,000,000 metric tons. There are 2204.6 pounds in a metric ton, so the weight of the Earth in pounds would be 13,165,871,200,000,000,000,000,000. A quick rule of thumb calculation (taking advantage of the fact that, in general, each higher size category is about one decimal place greater in size than the last, but correcting about once every eight places), enables us to place the Earth's D&D size category about 22 places beyond Colossal. From Medium on up, each size category in D&D can carry twice as much as the one before, so by following that trend we can deduce that an average-sized planet such as ours should be able to tote about 2^27 as much as a human-sized creature might, or from 4,429,185,024 to 5,905,580,032 without breaking a sweat, and up to 17,448,304,640 English pounds if it is willing to bear a heavy load. (I already did my part for the metric system by converting from metric tons to pounds, the trip back is left as an exercise for the reader.)
But not so fast. These figures assume that the Earth has an average strength score in the range of 10 to 12! D&D also assumes that this Strength scale is for a medium-sized creature. Larger ones get bonuses to Strength in addition to the greater carrying capacity. We'll use the entry for Hill Giant, the weakest variety of Giant, in the Monster Manual to deduce what the Strength score for the Earth should be. (Thank the gods that all monsters now have complete average ability scores in their manual entries!) Hill Giants are Large creatures, one category larger than Medium, and have an average Strength score of 25. Assuming that 11 is the average for human size creatures, that's a difference of 14 points. Multiplying that difference by 26 and adding it in should give us a good average Strength score for a Very x23 Colossal creature or a Medium-sized planet. The resulting score is 311. A human-sized creature with a Strength of 311, according to the table in the Player's Handbook, can carry about 537,261,421,146,790,690,816 pounds – for a light load! A heavy load can be up to 6,456,360,425,798,343,065,600.
And finally, the moment of truth! Scale that figure up to take into consideration the extra size capacity to arrive at a final figure of about:
5,594,810,955,407,362,733,748,481,000,242,000,000,000,000,000,000,000 English pounds. Note that this is not a precise figure, as the Windows Calculator started dropping into scientific notation after the 30th digit.
No, I don't use any form of mind-altering drug! Why do you ask?