Don’t give toys that have a lot of loose parts, toys that make a loud or repeating noise, or stuff that spreads out. Thi KID might love it but the parents will hate you.
At one year old, he’s likely just getting his land legs. Check out push or pull toys as well as small scoot toys if you must get him a toy. As far as books go, picture books and ones that the text is rhyming or has funny sounds (Shel Silverstein and Dr. Seuss cometo mind and he’ll get them on a different level when he begins to read). Since you don’t live with him, you could go for a See-N-Say. 
With boys of all ages, you can never go wrong with trucks.
Babysitting vouchers for the parents.
What until next year to give him the loud toy with the repeating sounds which will drive his parents nuts. He’s too young for such subtleties, yet, and won’t play it for months like he will next year.
If you feel like you can do it annually, and you’ll do it for any other nieces or nephews in your life, I’d just start him an education fund and contribute money. I have a 3 year old niece and a 1 year old nephew, and I give $100 per birthday/Christmas (their mom and dad manage the RESP, and other family members contribute as well). As the kids get older, and they understand/appreciate gifts, I might also get them something small.
Books, books, books. At that age, the kind that cannot be eaten or otherwise mutilated.
They do have cloth books that would hold up best to a one year old. However at one year their attention span is short so I thought the box of Kleenex was a great idea…fun for the whole family.
If they celebrate Christmas, and if they haven’t already acquired one, a nice stocking, the sort of thing he can hang up for years and that came from Uncle so and so, might be nice. That is the kind of thing that I like to have but can’t bring myself to spend money on, so it makes a nice gift. For much the same reason, “occasion” clothes are nice even if a kid has plenty of functional stuff.
One of the gifts I gave my great nieces (twins) for their first birthday was this. One of them, at least, really liked it and Dad sent me a short AVI clip of her dragging the thing around.
One of those baby books about shapes or colors or something like that should be fine. The grown-ups can read it to him later. Your nephew’s main enjoyment will come from making a huge mess with the cake that is served him.
Maybe a subscription to a magazine for that age, such as Babybug or Highlights Hello.
One year wants nothing of course; at this point you’re trying to make the parents happy.
My two cents worth of suggestion is to get him a cute little Santa hat. he won’t notice or care, but his parents will probably think it’s adorable.
Since his birthday’s near Christmas, how about a special tree ornament?
Gee thanks. Now I have a nearly uncontrollable urge to go get a tissue box and start yanking.
I’m seriously thinking “well, the one in the bathroom is nearly empty, so maybe I could just do that one and it wouldn’t be such a waste…”
I limited myself to 5 yanks.
Was it everything you hoped it would be?
No. I wanted that 6th kleenex really bad. Juuuust one more…
I literally lol’ed. :D:D:D