Are anime budget and worldwide gross data publicly available? On Wikipedia there are two lists about box office bombs and highest-grossing films. On nearly every movie page on Wikipedia, there are two values: budget and box office, showing how much a film costs and how much it yields.

Is there something like this for anime, considering home videos, worldwide licenses and/or merchandising?
I doubt that the budgets are available for every series. Studios rarely have any incentive to release these numbers, and it could make fans angry if they think the studio isn't giving their favorite series a big enough budget. 

I was able to find some information. A single episode of anime generally costs around 10 million yen (see here or here, roughly $115,000 USD), though the exact number varies depending on production quality, voice actors, licensing fees, and other factors. The best I've been able to find is this, which really only has a few anime series from 2005 and earlier, and also includes a lot of western animation.

As a note, sales figues, unlike production figures, are widely reported. This forum thread has a lot of data related to that. This gives a sort of upper bound on the production costs, but it's not usually very accurate. For instance, the first season of Fate/Zero sold 52,133 bluray boxes at 39,900 yen each (roughly $496 USD), so the total revenue is about 2 billion yen, which for a 13 episode show corresponds to 160 million yen per episode. That's certainly way more than they actually spent.