It's a personal question, yes, and there should be no definitive answer (imagine, in the future, some well-intentioned moron pushing legislation to restrict it), but I think it's a topic worth mulling over in an age where most of our art criticism has gone online and is "print-worthy" within a blink of an unedited moment.
If a writer has the intention of taking a publicly-critical look at an artist's work, then my quick answer to the above question would be "none; no relationship". That's easier said that done, of course, but it seems to me that the relationship between artist & critic should be similar to that of politician & journalist. No, I don't mean deep probing or investigative research or on-the-spot questioning of just another private citizen, but, as is the case when journalists become too close with public servants, the critical blinders can go on and the tough things that must be said can get swallowed.
Take Roger Ebert. Recently he gave the new Alex Proyas movie, Knowing, a four-star rave. Big deal. He loved, I didn't. But the first thing that popped into my head was "Hmm... Roger Ebert did the commentary track on the DVD for Proyas' Dark City. They must have some kind of friendly relationship, yes?". The point is, I couldn't help but wonder if Ebert's reading of Knowing was somewhat skewed by him knowing Proyas. To be fair, Ebert hasn't given Proyas' career a four-star pass (he was critical of I, Robot), but for a movie that seemed to be getting universally ripped, Ebert's lone positive voice noticeably stood out.
Look, we all have biases, and I'm not saying artists and critics shouldn't be friends or lovers or etc. That's silly. But I DO think - as industry professionals - both parties should try their best to not swap spit when it comes to their jobs. And in the age of online movie criticism, the "job" of movie critic is becoming ever more blurred. Sites like AintItCool, Cinematical, Indiewire, SpoutBlog, and Bloody-Disgusting are some of the most frequented film sites, yet the reviews on those sites seem to be more promotion-driven than insight-stirring. Some of the writers for those sites even seem to get pretty buddy-buddy with the filmmakers they end up reviewing movies of.
"Who cares!"... "what a waste of breath!"... "loser", some of you may be saying. I get that. I understand, that to some people, the role of movie critic may be on par with that of IRS agent, but it's something I love and it's something I think is worth keeping as pure as possible.