Is there a comprehensive list on the web of all kosher products?
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I think the consensus will be that the answer to your question is 'no'. However, many certifying agencies have lists of all the products they certify, so a comprehensive list of @yydl's item #2 could exist by interpolating all of those that are available.
What you're asking for is huge. So huge, I honestly doubt it really exists. Here's why...
You must understand that there are a number of reasons something might be Kosher:
If you really want #1, you can ask this site for a list of foods that don't require a hechsher. It's actually not that big, but it will be location-dependent. (I may have touched upon it once over here)
If you're asking for #2, that would be something you can get from the certifying agency itself. For example, the OU has an online database (although some items are not in it). I don't know about others, but each agency is independent. Which means compiling a full-list would be super-tedious.
And finally #3, depends on your level of trust with said neighbor. And if it's you who's making it: knowing things about not mixing milk-and-meat and the like. For example, when following a recipe you find, recognizing whether it's Kosher or not by looking at the ingredients.
I don't know of any world list - especially since certain products are kosher in one country but not another - but some countries do keep lists.
Here in England we have a kosher guide and there is a product search online at http://www.theus.org.uk/jewish_living/keeping_kosher/keeping_kosher/kosher_product_search/
I think this can help:
Kosher Register http://kosherregister.com has a comprehensive list of kosher products by categories.
To make your search easier the website has a good search engine of kosher products: by category, year round, kosher for passover, food service and retail.