I have build the following code in a docker container with the following architecture:
cat /proc/version Linux version 3.16.7-tinycore64 (root@064f0e1ce709) (gcc version 4.7.2 (Debian 4.7.2-5) ) #1 SMP Tue Dec 16 23:03:39 UTC 2014

package main

import "fmt"

func main() {
    fmt.Println("Hello")
}

The binary distributed, runs with no problem on a busybox container, with the same architecture without installing golang.

The problem

When I do the same for the following code:

package main

import (
    "fmt"
    "net/http"
)

const (
    port = ":80"
)

var calls = 0

func HelloWorld(w http.ResponseWriter, r *http.Request) {
    calls++
    fmt.Fprintf(w, "Hello, world! You have called me %d times.
", calls)
}

func init() {
    fmt.Printf("Started server at http://localhost%v.
", port)
    http.HandleFunc("/", HelloWorld)
    http.ListenAndServe(port, nil)
}

func main() {}

Then I get:
ash: ./hello_world: not found

I might be missing some dependencies - like "net/http"?
But I thought the go build would build all into the binaries.
This is for both go build & go install.

Any idea?

The answer is most probably the one described in this article.

Some critical parts of the standard library use CGO [...] if you cross-compile Go to Darwin or Linux your programs won’t use the system DNS resolver. They also can’t use the native host certificate store. They also can’t look up the user’s home directory, either.

And CGO links against some standard system interfaces by default, dynamically.

The article suggests using gonative to fix the problem. If that's not your cup of tea, some people suggest using:

go build -ldflags "-linkmode external -extldflags -static" 

Also read: https://groups.google.com/d/topic/golang-nuts/H-NTwhQVp-8/discussion

I think you need to disable cgo and build with netgo flag :

The net package requires cgo by default because the host operating system must in general mediate network call setup. On some systems, though, it is possible to use the network without cgo, and useful to do so, for instance to avoid dynamic linking. The new build tag netgo (off by default) allows the construction of a net package in pure Go on those systems where it is possible.

The netgo tag requires version 1.2 and above.