For basic living I would say:
1. Collars/leashes. I would recommend biothane collars, such as Gun Dog Supply Tufflex biothane collars with the free brass nameplate as they are cheap, won't absorb odors, waterproof, and easy to clean with a wet rag.
2. ID tags- I would recommend Boomerang tags for people on a budget or those who hate the dingling noise of tags (they have slide on ones) and I believe they have a lifetime guarantee. For those that want cute/funny tags I would suggest fetching tags or aggies anvil tags.
3. Kongs- excellent if your dog is being annoying and you are too busy or lazy to go do something with them, you can freeze things in them and let your dog have one and you get a break, it's good mental stimulation for them.
4. Clickers- I just love clickers and think they make training easier.
5. Small high value treats, such as zukes minis- although I wish the ingredients were a little better, for getting behaviors.
But then there are other things I would always recommend, like crates, stainless steel food and water dishes, etc.
I recommend different more specific things depending on what the person wants to do with the dog (hiking, serious training, sports, etc). But the things listed above are just basic things I think most could use.
1. Stibbar soft braided leather Leashes - SO nice. Got them for their birthday present.
2. Tiny stainless steel CAT food bowls. - My dogs have BIG ears and they end up dipping them in the larger style dog food bowls - LOL
3. Sleeping crate with an exact MATCHING SIZE PAD!
4. "Cowboy Magic" detangler - no more cutting out the mats.
5. Pure Paws H2O Shampoo and Conditioner. Smells great, feels awesome.
Honorable Mention - Doo-doo bag dispenser that attaches to the leash. Never need to forget them again.
Martingale collars - my big-necked, small-headed dogs can't back out of them
water rover water bottle for dogs - great for walks
himalayan chews - keeps everyone busy
ID tags/microchip - because I want them back
obedience classes - all my dogs take classes for basic manners
For a puppy or dog that isn't already trained: a crate
For dogs in general:
Sturdy leash - I've never used an Ella's Lead but know they have great reviews
Quality food - recommendation would vary but choosing a high quality food is going to save your dog's health and you on vet bills in the long run
Those are really my only three. Maybe some kind of car restraint if you don't use a crate in the car?
For dogs with specific needs I have a lot of different products I'd recommend. I recommend a head halter to a lot of clients who have trouble managing walks while in the process of training, Cuz toys for training toy-motivated dogs, various puzzle toys for dogs that need the extra stimulation or are home alone frequently, etc.
1. Wire crate - my big hairy guy gets too hot in a plastic crate, which exacerbates his dislike.
2. leather lead. Love my 1/2" leather lead from Bold Lead Designs.
3. Kongs - I stuff about 10 at a time and pop them in the freezer. Wonderful.
4. Bully Sticks - most favorite chew for my puppy.
5. Waterless shampoo - using One Shot Dry Clean Spray right now for my Bouv. He's way too big for me to bath at home, and his coat takes hours and hours to dry without a heavy duty dryer. Love the mild minty scent of One Shot, and it seems to do a great job of cleaning and freshening his coat.