Well from personal experience....my current best friend is of the opposite sex...and his wife is totally fine with it. It shows that we all have a healthy respect for one another. I respect the sanctity and importance of their marriage to never even let any kind of inappropriate feelings develop, which...no offense to him, wouldn't probably happen anyway lol I view him as the amazingly awesome brother I never had. And I love the fact that his wife trusts me in that manner instead of being a typical paranoid, jealous, and skeptical female.
If, however, there was some level of discomfort on her part (and especially on his part)....there should always be respect shown. The wife should be respectful enough of her husband to explain her uneasy feelings, the husband should respect his wife's feelings and the third party should also realize that sometimes it can be a tricky situation. I think a compromise is POSSIBLE in such situations....perhaps limiting the amount and type of contact that takes place (i.e., never being alone together, not spending hours on the phone with the 3rd party, etc.) but sometimes such a compromise isn't possible. If it is not, then you must ultimately do what you need to do to preserve your marriage if you truly love one another. You have made a lifetime committment to your spouse and should honor and love them enough to be willing to give up a friend if it keeps the peace. HOWEVER...I PERSONALLY do not feel that anyone should be so insecure as to demand that their partner get rid of a good friend, simply because they are paranoid.
At any rate....it is VERY possible to have and maintain healthy, beautiful and fulfilling relationships with those of the opposite sex (or same sex, as was mentioned, if you're not hetero). Everyone just has to be realistic about the situation and about their own feelings.