I run a free service (http://eve-central.com - I am not a designer ;)) which has an open API - no rate limits, no accounts, no signups, etc. Yes, technically this is bad, and has had interesting implications for support (some APIs date back to 2007 without any changes), but in this case is the right choice. It works by throwing enough power behind it, and relying on caches. The API is popular for its audience - approximately 50+ million calls per month, which easily outnumbers the (ad supported) web front end pageviews.

Due to licensing of content, it would be iffy to monetize directly (technically even the ads are in violation of that), so I don't even consider it.