My thoughts on opposite sex friends while in a relationship:
Mutual friends are okay for the most part. Exclusive opposite sex friends, I really don't think they are a good idea in most cases if it can be avoided. Even if it is completely non-sexual in nature, it will cause unneeded stress on your relationship. Please note that my thoughts are only geared to very serious relationships, which it appears you are in.
And for those that say "I've been best friends with so and so since grade school", well ythen You should've been with that person anyways! Your significant other is darn right to be jealous/upset, because sooner or later that realization will come to you or the friend, and there will be a serious problem. There is not room for both your "Best friend/GF/Fiance/Wife" and "the other best friend."
Warning: Long winded H.S. sap story ahead!
I had best a friend that was a girl, her name was Kristin, thru middle school and high school. I was attracted to her - damn I idolized her. I never thought she was interested in me though, so I never pursued except for an awkward hand hold attempt in Alien Encounter at Disneyworld my soph. year.

She started dating another guy and killed that. I dated my future wife, Michelle, thru Junior / senior years, with a breakup mixed in junior year for good measure. During the breakup, I spent alot of time with Kristin. We sat together on the bus ride to Florida during the years band trip. It was then that I came to the realization that I no longer had any romantic feelings for her, and that she was a sister figure. Michelle was always VERY jealous of her, but mostly tried to keep it to herself. I kept in contact with Kristin thru college. Whenever we met up, there were hugs, chit chat, etc... for me only, as her and Michelle were never friends or acquaintances of any sort. Michelle would raise her concerns to me and I would blow them off, because I knew there was nothing there. We had fights over it off and on. I finally decided that the friendship wasn't worth the drama, so I kept out of touch with Kristin. Sure I arbored a bit of resentment, but I tried to see things from Michelle's point of view. Now that I look back, it is quite obvious that Michelle's concerns were quite justified.
Now that I am older/wiser and know the evil ways of women, I know for a fact that Kristin was interested in me - and more so after High School. It was never meant to work out though I suppose. I have no resentment at all, and know that I am with the person I am supposed to be with. I also know that if you are in a serious relationship and another girl is trying to be your friend and be in your life, 99% of the time it is involuntary bitchism causing her to just try and make your wife jealous and prove to herself that she can work her magic. Learn how to identify this behaviour, that way it does not cause you undue stress.
Long story short: You can't have both and be happy. If your significant other is acceptive of it, then she is either lying, or is cheating on you.
