How do you make sure that everyone understand that that equipment belongs to you and not The Company? I'm currently resorting to printed labels of my name or initials, but I can't help but consider that that's a tissue defence.
For BYOD laptops/PCs, keep the receipt (which will usually include the serial number) and store a photocopy at the office in a place where you can easily keep track of it. If it's something shipped direct from the manufacturer, keep the box with the shipping label on it as additional evidence. You can also let your manager know that you have equipment that you personally own on-premises and give him an itemized list with serial numbers. For small items like mice, keyboards, etc., they're generally not worth enough to lose sleep over if lost.
Beyond that, the general rule of never bringing anything to work you're not willing to lose applies. Just like any other kind of BYOD device, your employer is not going to reimburse you if your personal hardware is stolen or accidentally damaged, so take appropriate precautions.
Lastly, make sure that you secure _and_ backup data on your hardware at least as well as your IT team does for company issued hardware. Your manager is not going to be at all sympathetic if you lose work due to a hardware failure on your BYOD device or due to malware.