While there are efforts to create meaningful definitions and systems for vegan certification, currently there are no internationally, or even federally regulated standards or definitions of what makes a product vegan. This is true for vegan condoms.
The main issue for vegans around condom manufacturing seems to be about the product casein. Casein is a milk protein that is used in the manufacturing of latex for condoms. Vegans on the whole dont use milk products or by-products.
There are three latex condoms on the market that dont use casein in the manufacturing process.
RFSU is the Swedish Association for Sexuality Education, a very old sexual health organization that has a line of condoms which are vegan. These condoms are available in the U.S. at select retailers in a few different styles.
Condomi is a large European condom manufacturer that uses cocoa powder instead of casein. Unfortunately these condoms are not currently available in the U.S. or Canada. They were for a time, but I have heard that the manufacturer is now working towards meeting U.S. requirements for sale (this is not a safety issue as I understand it).
Glyde condoms are available in the U.S. from several retailers and they are also vegan. So for now this seems to be your only option.
Another Concern for Vegans?
I also wonder about whether or not vegans need to be concerned about the lubricant in condoms. In most cases, this lubricant will contain ingredients that were, originally, tested on animals. While the condom companies will not have necessarily done this testing, I presume that some vegans would prefer to stick with non-lubricated condoms, to avoid this possibility.

