In Canada, ALL insulin and syringes are available as over the counter medications. In the US, the non analog insulins can be purchased without a valid prescription. In the UK, ALL insulins require a prescription, and in most if not all EU countries, ALL insulin also is Rx needed.
Some countries also require a prescription for insulin syringes and/or pen needles.
In the US, whether or not you need a prescription for syringes/pen needles is determined by state, not US, law. The laws of your state will apply re: syringes/pen needles requiring a prescription. If you order syringes or pen needles online, the law of the state where you're ordering them from will apply. If you order from a business whose state does not require a prescription for syringes or pen needles, you will not need one, even if the laws of your state of residence say you do. Conversely, if you live in a state where there's no mandatory prescription for syringes or pen needles and order from a company in a state where a prescription is necessary, you will need one to do business with them.
The difference here, for those in the US regarding insulins and syringes is that federal law (US-FDA) regulates which insulins are prescription required, but state law governs whether one is needed for syringes and pen needles.
Even if you buy syringes and pen needles from a local pharmacy and don't live in a state which requires a prescription for them, the policy of the pharmacy itself may be to require a prescription for them.