A dirty solution to make newline pastable again:

// Use InputFieldM instead of InputField
public class InputFieldM : InputField
{
protected override void Append (string input)
{
if (HoldKeyManager.HoldCommandOnly && Input.GetKeyDown (KeyCode.V)) {
TextEditor te = new TextEditor ();
te.multiline = multiLine;
te.Paste ();
input = te.content.text;
}

if (TouchScreenKeyboard.isSupported)
return;

for (int i = 0, imax = input.Length; i < imax; ++i) {
char c = input [i];

Append (c);
}
}
}

If Unity team couldn't/wouldn't have time to get the InputField right, just make every function and member of the InputField object overridable(declaring functions virtual and members protected or public instead of private) so people who needs customized behaviour can write their own functionality by inheriting InputField.
Also, please liberate the use of GUIUtility.copySystemBuffer to developers. A better cross-platform copy and paste solution would be much better.
General advice: UI components are usually very customized. Instead of taking a closed approach of assuming many feature or behavior for developers, try opening up more API and settings of components. E.g. copy/paste keypress can be an event that allow developer to customize response; replace '\n' with space? why space?

Details on why newlines are replaced with space lies in code below:

// ----- InputField.cs ------
static string clipboard
{
get
{
TextEditor te = new TextEditor();
te.Paste();
return te.content.text;
}
set
{
TextEditor te = new TextEditor();
te.content = new GUIContent(value);
te.OnFocus();
te.Copy();
}
}

// ----- public class TextEditor ------
public bool Paste ()
{
string text = GUIUtility.systemCopyBuffer;
if (text != string.Empty)
{
if (!this.multiline)
{
text = TextEditor.ReplaceNewlinesWithSpaces (text);
}
this.ReplaceSelection (text);
return true;
}
return false;
}
// ----- End of code reference -----

*I suspect InputField.cs is written by an intern.

This is really quite easy to reproduce and is extremely annoying. What good is a text field if it doesn't work?

Sorry, it's my own problem that '/' is ignored. '/' should be fine.

'/' is also ignored

Copy & pasting text from outside of Unity (such as notepad or a website) into an inputfield at runtime then any newline characters are removed by unity!

Something similar seems to be happening in Unity 5.1.0f3

Something similar seems to be happening in Unity 5.1.0f3

Tabs are also ignored