My opinion: if the person you are currently with has an issue with seeing pictures up of you and your old flame, this is a RED FLAG, my friends! While I don't recommended keeping a framed picture of you and your ex boyfriend/girlfriend kissing on your nightstand, your new beau or beauty should be more or less content with coming across old pictures of you two together. If this sends them into a hissy fit, most likely there are many more hissy fits to come and early on is when you want to address this and decide if it is something that can be fixed or something that you are willing to put up with.
One of two things could be occurring here. Either:
a.) The person not OK with seeing the pictures up is overly jealous and is the one in the wrong
b.) The pictures are indecent/inappropriate and they should have never been up in the first place
If the pictures are lewd and inappropriate, then they never should have been made public in the first place, and the issue is with the now questionable one who to allowed them to be visible. This is now a RED FLAG with the person in the photos, and chances are you (the offended one) are now in over your head and should have realized this sooner in an ideal world. If they are skanky pictures, it's not the pictures you should be worried about its the fact that they were taken and posted in the first place!
If the pictures are generally tasteful, but they are of two people who used to be together, I say it is perfectly OK to let them stay up. If the new person cannot handle seeing them, this signifies underlying insecurity and jealously issues and in most cases will only continue to grow into a bigger beast with time. I say address the jealousy NOW and if it cannot be resolved, you might want to consider moving on.
Confidence is attractive, remember that. I'd even say it is the #1 most attractive thing about a person. There's nothing more repulsive to me than the memory of one of my old flame's jealous and insecure hissy fits over whatever it was he was upset about years and years ago. And, if you are the one being bothered by this, perhaps if you re-think whether or not you are being irrational you can save yourself a great deal of unecessary heartache. Ex's are ex's for a reason! Keep your head up and even fake it a little bit if you have to...don't ever let them see you sweat. You should be able to deal with the occasional picture or run-in with the ex, and your confidence will only boost your value in your new relationship.
[Old Pictures, Great Memories]