Having been to Amsterdam numerous times, there's not really a north from there.

It's mostly land reclaimed from the sea.

Is there some place you want to go?

They could go towards Norway!

So OP you have to expand on this.
Details required from you:
Time of year?
Method of transport?
Likes/dislikes?
Length of trip?
Do you have to go back to Amsterdam?

I would like to go in early July, would like to go to Norway, Sweden, or Denmark. I would prefer to rent a car. Don't know anything about the transportation system in that part of the world. I would like to spend about two weeks there. Going to London will be my ohter option. I don't need to go back to Ansterdam. Thank you very much for your suggestion.

If you don't go back to Amsterdam, don't hire a car - you'll be paying a lot in dropoff costs. Personally, when going to Norway or Sweden, I'ld probably fly.

Denmark by train perhaps (if you can find a good train connection).

Fly. It's too far for a road trip. If you have plenty of time, you could consider driving to Kiel to take the ferry to Oslo, then drive down to Goteborg, take ferry back to Denmark or some such, then drive back. The drive to Kiel is about a day. To Hirtshals a long day.

Two weeks is too short. Go to Scandinavia instead.

I like Hoorn, Zwolle, Lelystad then Bremen and Hamburg looks good as do the towns of "riddle of the sands"

Don't forget Groningen, then one of the Frisian Islands, then follow the coast to Hamburg.

Indeed the Frisian Islands are nice. They are called Vlieland (very small, no cars allowed, with one little village), Terschelling (my favorite, a few nice villages and big enough to visit a few days), the ferry to these islands departs from Harlingen. For more information:
http://www.rederij-doeksen.nl/home?format=html&locale=en or www.evt.nl (They are much cheaper, but their site is only in Dutch, click 'boeken' to purchase tickets, no cars allowed on board).

Another Frisian Island is called Ameland (a few villages, smaller than Terschelling, nice for a one-day or weekend stay). The last very very small Frisian Island is called Schiermonnikoog (this is a Island that's mostly visited by people that really like nature, wich btw is beautiful) The ferry departs from Holwerd. For more information check: http://www.wpd.nl/en/ (shorter trip than from Harlingen, so much cheaper)

All of the Islands have good bus transportation. See: http://9292.nl/en (good site to check all transportation in the Netherlands).

"The drive to Kiel is about a day"
From Amsterdam? Nah... 5 hours is hardly "a day", is it?

If you like driving, you could drive to Travemunde (Lubeck), take the nightboat to Trelleborg from there. Explore the south of Sweden, if you have enough time even visit Varmland. Than go back via Gothenborg, take the boat to Fredrikshavn, slowly go south through Denmark, northern part of Germany, back to the Netherlands. Groningen, Friesland, Afsluitdijk, Amsterdam. But you'll be doing a lot of driving...