Can I accept bitcoin tips or donations in my free Android apps & widgets?

I don't know what Google's official policy is for certain, but a donation should be no problem. In theory.

• http://play.google.com/about/developer-content-policy.html only mentions that any purchase of in-app benefits must be handled via Google's in-app billing system.
• https://play.google.com/about/developer-distribution-agreement.html#pricing-payments says essentially the same in legalese.

So as long as donors do not buy/gain anything, not even a thank-you or honourable mention, and that is made clear in your app, you're in theory safe. Disabling ads for donors is for example easily a violation of those terms.

The rules are however Google's to interpret and enforce. And sentences like

The Payment Processor must process all fees a Developer receives for any version of a Product distributed via the Store.

in 2nd link can easily be applied to donations if the app-review person sees fit, even just because he/she misinterpreted the donation button or

If Google decides that your donations are actually fees, they can & will suspend your app (probably without prior warning & time to fix the problem). There are cases of this you can find on the internet.

There is an appeals form you can find here: https://support.google.com/googleplay/android-developer/answer/2477981 but the answer in practice seems to be "No. Don't ask again.".

Also be aware that Google counts violations and can ban you as a person (not just your current account) from publishing apps on the Play store.