Relationships are dynamic; constantly growing and changing. So a relationship in which no one changes is headed down a boring path. Who wants to do the exact same things in the exact same order every day? Who wants to consistently get angry at their significant other for the same stuff every day? There's no way a stagnant relationship can be a happy one.
Are you the same person you were a year ago? 5 years ago? I'm sure you've retained your strongest personality attributes, but I highly doubt you're still walking around speaking like Borat and dancing to "Sexy Back" every night in front of your mirror (yeah, it's been five years since that stuff!) The fact is you have changed. You've likely dropped some bad habits and switched them out for some good ones. Knowing this, I fully support changing for your significant other, to a certain degree. I'm all for changes like expressing some interest in his or her favorite sport, committing to an active lifestyle, trying new foods you think sound disgusting, promising to put your dishes in the dishwasher not the sink, etc. I could list all kinds of little changes. Making efforts like these every day proves the depth of your feelings. It proves that you care for him or her so much that being in the relationship makes you want to be a better person each day.
What if he or she wants you to change something that is super important to you? What if your religion is different, or your job is going to take you across the country? Then what do you do? These kinds of changes can be deal breakers. These are things that are a core part of you. When one member of the relationship asks the other to change a core part of his or her life, I fail to understand why they are together.
Let me give you an example. Let's say I meet this guy who is awesome. Everything about him is great, he's attractive, he a genuinely good person, and we plan to settle down in the same city. Then, shortly after meeting him he tells me he's an atheist. That is a huge part of someone. Religion is definitely a deal breaker. No matter how amazing this guy may be, I will not be satisfied dating an atheist. I would spend every day wishing he wasn't an atheist. I would undoubtedly end up nagging him and ruining any chance of a happy relationship. This is when asking someone to change that drastically is a bad thing in my mind. If something that important is not working for you, then I say the relationship is not meant to be.
There's always the possibility that he or she says they need time to change. They want to change but need to take it slowly. Personally, in that case I would say get at me when you're different. I know myself enough to know I won't be happy until then.
To boil it down to the essentials, it's okay to ask someone to change something they do. It's probably a bad idea to ask them to change who they are. After all, why would you want to date someone if you don't like who they are?