At work we make websites for other companies. One of our client wanted us to make a e-commerce website for them. Nothing out of the ordinary until we realized they had 50 000+ products to sell and their classification is inexistant. In other words, we don't have ay categories to work with. They just told us to "Put a search bar and it'll be fine".

So, how would you make an e-commerce site work for the users without any kind of browsing through lists of products ? 

**EDIT**
The client is a reseller. He sells power outlets, light bulbs, electrical cords and stuff like that. The reselling part is why he doesn't have categories, because every single seller manage their own database with their own description for each product.
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I would recommend a [masonry-like](http://masonry.desandro.com/) experience as Pinterest implements. Infinite scrolling of all 50k products and have a details page for each one. Keep track of which products are viewed the most on a weekly basis and display those towards the top.

It sounds like this client wants an adventure-like experience with a search bar that searches on just one field; product name.

That is my 1/50th of a dollar; 2 cents =)
If there is no way of categorizing the products then search must be the primary method of traversing the catalog. But as a previous answer suggests you should guide the user with top products sold for a search, top products viewed for a search etc. The other users behavior should help guide them, consider adding a method for users to tag products to build the categories may be an option. You may also be able to build a straw man structure by querying the product names for things like bulb, switch, socket etc and start with that to see what sort of a category structure may be involved.