Can I list all standard Go packages?

You can use the new golang.org/x/tools/go/packages for this. This provides a programmatic interface for most of go list:

package main

import (
    "fmt"

    "golang.org/x/tools/go/packages"
)

func main() {
    pkgs, err := packages.Load(nil, "std")
    if err != nil {
        panic(err)
    }

    fmt.Println(pkgs)
    // Output: [archive/tar archive/zip bufio bytes compress/bzip2 ... ]
}

To get a isStandardPackage() you can store it in a map, like so:

package main

import (
    "fmt"

    "golang.org/x/tools/go/packages"
)

var standardPackages = make(map[string]struct{})

func init() {
    pkgs, err := packages.Load(nil, "std")
    if err != nil {
        panic(err)
    }

    for _, p := range pkgs {
        standardPackages[p.PkgPath] = struct{}{}
    }
}

func isStandardPackage(pkg string) bool {
    _, ok := standardPackages[pkg]
    return ok
}

func main() {
    fmt.Println(isStandardPackage("fmt"))  // true
    fmt.Println(isStandardPackage("nope")) // false
}

Use the go list std command to list the standard packages. The special import path std expands to all packages in the standard Go library (doc).

Exec that command to get the list in a Go program:

cmd := exec.Command("go", "list", "std")
p, err := cmd.Output()
if err != nil {
    // handle error
}
stdPkgs = strings.Fields(string(p))

If you want a simple solution, you could check if a package is present in $GOROOT/pkg. All standard packages are installed here.