A few orders of magnitude more than 3.06*1018.
All of the above writeups are missing something crucial in their calculations. In the Catholic doctrine of transubstantiation, the eucharist actually becomes the blood and body of Jesus Christ. We can't forget to account for all of that additional biomass in calculations; I've done some new ones below.
Bear in mind that this is all back-of-the-envelope calculation, and doesn't pay much attention to real scientific conventions. Consider yourself warned that the error may be two or three orders of magnitude.
Lets assume 2 grams of wafer and 10 grams of wine per communion, a light wafer and a small sip. We'll also assume that upon transubstantiation the wafer and wine don't turn into any specific body part or muscle group, but instead into sort of a uniform Jesus slurry. That is, we're going to assume that the liquid to solid ratio of the human body is the same as the wine to wafer ratio found in communion.
To count the number of atoms in each serving, all we need is some high-school level chemistry. We're first going to find how many grams of each element appear when the serving is transubstantiated, using percentages from delld's writeup under Human Body Composition. For simplicity's sake, the 1% of the human body made up of trace elements will be ignored. Using those figures along with the Periodic Table of the Elements, we'll convert from grams to moles. Since moles count the number of atoms in a given mass, we'll have the total atomic count of each communion after all of this calculation.
61% oxygen --> 7.32 g --> .456 mol
23% carbon --> 2.76 g --> .230 mol
10% hydrogen --> 1.20 g --> 1.19 mol
2.5% nitrogen --> 0.300 g --> .0214 mol
1.4% calcium --> 0.168 g --> .00419 mol
1.1% phosphorus --> 0.132 g --> .00426 mol
99.0% wafer mass --> 11.880 g --> 1.90585 mol
Ok, wonderful, now we know how about many atoms of Jesus are created every time somebody takes communion. This by itself means little as communion is taken every day all over the world. Unfortunately, I haven't the statistical insight to calculate how many communions have been taken since the beginning of the Catholic church. Instead we'll calculate how many Jesus atoms are created in a year, to give us a very rough idea of what the total would have to be.
As of 1998, the baptized Catholic population of the world accounted for 17.4% of its total population -- or 1.0266 billion people. If each of these people take communion once a week for a year, that's (1.0266*109 people * 11.880 g * 52 weeks), or about 634,000,000 kilos of Jesus consumed every year. Notice that the 64 kilos or so of original Jesus biomass are utterly irrelevant with regard to this. Using our previous calculation, that's about 101,700,000,000 moles of atoms of Jesus created in 1998.
Using cordelia's figure of 5*1018 moles of biomass, we see that this conversion accounted for 2.035*10-8 percent of earth's biomass in 1998. This is still almost infinitesimally small, but much much larger than cordelia's estimate. We also find that the number of Jesus atoms eaten every day if the Catholic church had only existed during 1998 would be (250 moles * 2.035*10-8 * Avogadro's Number) = 3.06*1018, a drastically larger number than the cordelia's estimate.
Interestingly, but somewhat off topic, transubstantiation means that eventually the earth's entire biomass will be made out of Jesus. Assuming the 2.035*10-8 percent change stays constant, it will be (100 / 2.035*10-8) = 4.91 billion years until that happens. If the sun hasn't killed us off by that time, the environmental balance change due to all of that extra oxygen and calcium probably will.