There are certainly positive rights that could be net beneficial. And taking away negative rights could also be helpful. E.g. the negative externalities of imminent domain could be reduced by censoring anyone who tried to talk about how it's a bad deal -- this would temporarily reduce the negative effect on real estate prices. But it sets bad precedents and leads to bad decisions.
But we have a right to health care, at least where I live, and I'm not aware of doctors' rights being compromised. Nothing's forcing them to work for the National Health Service.
That sort of right merely compels the government to implement certain policies (i.e. hiring enough public sector doctors).
I was thinking more along the lines of anything tax pays for (so yes, healthcare does work as an example, but not in the way you suggest). Presumably, taxing people is a violation of their negative right to be left alone. Yet tax pays for many good things, and I don't want to live in a place where it doesn't exist.
Houw about three really good/strong examples?
I'll even stipulate one - trial by jury with competent representation. (I'm pretty sure that health care won't qualify.)