Collections

If it is a positive entry, then I feel you should let them remain in your credit report as it will help you increase your credit scores. As far as the negative entries are concerned, if you have paid them off, then you can contact the creditors/collection agencies and apply for deletion of the account by writing a pay for delete letter. But it would have been better if you could have negotiated with the creditors/collection agencies regarding pay for delete before you paid them off and got it in writing.

Some times it so happens that you make late payments under circumstances when you face financial hardships. But once you've paid for it, the collection agency or the creditor is expected remove the listing if you'd otherwise been a good customer with them. So, if your account is now paid off, you may try sending them a Goodwill Letter and check if they remove it solely out of goodwill. Here's a sample goodwill letter for you - http://www.debtconsolidationcare.com/letters/goodwill-removelisting.html

Once a debt is paid, you no longer have payment to offer in exchange for CR deletion, so a PFD letter would not be appropriate.
After payment, you can send a good-will letter asking for CR deletion of the collection.
There are two hurdles in sending a GW letter to a debt collector.
First, it is against their written credit reporting agreement with the CRAs to delete prior, accurate credit reporting based on payment of the debt. Somce debt collectors adhere to this stringintly as a matter of policy, while some others will still delete.
Second, unlike GW letters to a creditor, who may still want your future business, debt collectors thrive on your misfortune. They have nothing to gain by granting GW deletions.
It never hurts to throw together a GW letter and send it out.