You could use the DoDirectPayment API to process payments. This will keep the buyer on your site, and they will enter in the information on your site. Then you will pass the details over to PayPal through an API call, and PayPal will then send the response back to you if the payment is approved.
If you are not wanting to use the DoDirectPayment API and are wanting to direct the buyer over to PayPal's pages to complete the payment but do not want to use Express Checkout, you could use PayPal Payments Adv/Payflow.