Can I ask my employer if I can work as a contractor instead of an employee?
You can of course ask your employer anything you want. However I think you should reasonably ask yourself "what's in it for your employer?". I'm assuming that the things you find attractive are the higher pay, the flexible hours etc. They aren't necessarily things that incline your employer to agree.
Employers typically employ a contractor because either a) they want someone with a specific skill for a limited period of time (hopefully not your case) or b) the total cost of using the contractor is less than an employee. The latter is because of the things they don't have to pay the contractor for - sick time, vacation, health insurance. You have to remember that you will be expected to pay for these things, making the seemingly higher salary of a contractor much less attractive in reality. If you are willing to work for less total cost than the total cost of being an employee, that might be attractive to them. If you are a sufficiently valuable employee then your employer might agree to the switch simply to keep you happy.
Of course the other advantage to your employer of your being a contractor is that they can terminate you much more easily. If that's something that appeals to them you may be in trouble.
The nature of the work often will dictate if you can be a contractor or not. Sometimes the way you do your work or your working environment will rule out whether or not you can be a contractor.
As the other posters have stated, you can certainly ask your employer to do this. But before you do you need to have one or more solid reasons for requesting this. I say this because your employer is going to ask you very detailed questions as to why you now wish to change your working relationship.
While not having very good answers may not cause your employer to ignore your request, by making it and showing that you haven't weighed all of the potential risks and consequences before presenting it could cause your employer to reassess your current relationship. Is that something that you were willing to undertake, OP?
Also, when you become a contractor you lose a lot of the protections and benefits that you have when you are an employee. This includes unemployment compensation, workman's compensation (in some areas),vacation time and sick leave. are you willing to give up these benefits for what may result in becoming a glorified "temp job?"