I worked for vets for 12 years and the last vet that I worked for was more into fewer vaccinations for OLDER animals. DHPP we didn't feel was necessary for dogs that were, let's say, over 4 or 5. Typically the things that this vaccine protects against are typically acquired by puppies and younger dogs (even up to a couple of years).
The things that every pet should get (depending upon the area) is:
*Rabies- How often depends upon where you live. Many states, such as Alabama where this is a higher rabies epidemic, require YEARLY vaccines by state law. Many northern states only booster every 3 years. It's usually the same vaccination (there are those that are only good for a year, but most vets use the 3 year type), but legally you have to have it yearly in some states.
*Bordatella (kennel cough)- Super important if you ever board your pet or have them groomed, but important regardless. It doesn't cost much and this is super contagious and quite frankly, a pain in the butt if your dog gets it. Then you have to listen to a hacking dog that coughs up slimey stuff and if they do contract it then you're looking at a bill to see the vet and be prescribed a couple of different meds. No fun to deal with for either you or your pet.
*Heartworm test- Some vets will recommend every 6 months, but personally I do it yearly. This is important because you wouldn't believe the number of owners who accidentally forget a month, and although you rarely see it, I have seen pets who were on prevention year round and still contracted heartworms. Giving them preventative while they're positive can be very dangerous. I'm not sure of how this works now, but back when places like 1-800 Pet Meds, etc, came into play, heartworm manufacturers wouldn't foot the bill if you treated your dog monthly and they still came up positive if you chose to purchase from places like this. They DID pay for treatment for heartworm cases where the pet was taking the product monthly, purchasing it from a veterinary clinic, and was being checked for heartworms as recommended. I'm not sure if this is still true or not, but I did email one of these places recently to see what they had to say and they weren't sure how the manufacturer would handle it.