Yes, I do send a reminder and an invoice. When I have a booking, I put a reminder on my calendar to send an invoice several weeks before the final payment is due. Initially, I e-mailed the invoice 2 weeks before the payment was due, but I found everyone was late. Once I started sending the invoice and reminder 3 weeks before the due date, things started coming in on time. Once I receive payment, I mark the invoice paid in full and list their payments and send it back to them. So far, it's going very well.

I don't send a note until a payment is overdue.

I am likely in the minority of property owners and I would  advise sending out reminders - depending on how reliable your guests are in making payments and how you feel about allowing a few days or week leeway for payments.

I find my guests are generally very reliable and do not need reminders.

Also, with a seasonal rental, I usually have only sixteen to twenty parties on my annual calendar.  I have a simple payment structure (25% on signing lease, 25% on February 1, and the balance - 50% - and security deposit eight weeks prior to stay) and it's easy to track payments as they do, or do not, arrive in the mail.

When a payment does not arrive I write a brief email advising the party that my records indicate a payment is due and that I have not received it.  I usually include some news about my home or the area (update to furnishings, new restaurant, etc).  That's all that's required.  I get an almost immediate response that the payment will be sent and the check appears in the mail in the next few days.  Since it's usually one or two guests that overlook payment I don't see the point in sending an email to everyone.

I think a more active rental would require a more structured system.