Have there been any anime with actual product placement? In Steins;Gate, Dr. Pepper is mentioned several times as the "An Intellectual Drink, For The Chosen Ones".



I've seen a lot of other shows that have stores or products with similar names to the real-life brand, so that the producers can avoid copyright issues.




Even though the inclusion of Dr.Pepper wasn't asked for by the Dr.Pepper company, after the release of Steins;Gate the sales in Japan for Dr.Pepper shot up. ref. 

Have there been any anime where a company has paid for their product to be included in the show?
Yes. Sometimes it's a sort of "exchange" of product placement - the anime will show the brand in the show, and the brand will put something about the show on its products for a certain timeframe.

Code Geass: Pizza Hut

 

Rebuild of Evangelion

 

Tiger & Bunny: Various






I'm sure there are more examples but these are just a few.