How to properly highlight selected item on RecyclerView?

This is much simple way to do it.

Have a private int selectedPos = RecyclerView.NO_POSITION; in the RecyclerView Adapter class, and under onBindViewHolder method try:

@Override
public void onBindViewHolder(ViewHolder viewHolder, int position) {   
    viewHolder.itemView.setSelected(selectedPos == position);

}

And in your OnClick event modify:

@Override
public void onClick(View view) {
     notifyItemChanged(selectedPos);
     selectedPos = getLayoutPosition();
     notifyItemChanged(selectedPos); 
}

Works like a charm for Navigtional Drawer and other RecyclerView Item Adapters.

Note: Be sure to use a background color in your layout using a selector like colabug clarified:

<selector xmlns:android="http://schemas.android.com/apk/res/android">
  <item android:drawable="@color/pressed_color" android:state_pressed="true"/>
  <item android:drawable="@color/selected_color" android:state_selected="true"/>
  <item android:drawable="@color/focused_color" android:state_focused="true"/>
</selector>

Otherwise setSelected(..) will do nothing, rendering this solution useless.

UPDATE [26/Jul/2017]:

As the Pawan mentioned in the comment about that IDE warning about not to using that fixed position, I have just modified my code as below. The click listener is moved to ViewHolder, and there I am getting the position using getAdapterPosition() method

int selected_position = 0; // You have to set this globally in the Adapter class

@Override
public void onBindViewHolder(ViewHolder holder, int position) {
    Item item = items.get(position);

    // Here I am just highlighting the background
    holder.itemView.setBackgroundColor(selected_position == position ? Color.GREEN : Color.TRANSPARENT);
}

public class ViewHolder extends RecyclerView.ViewHolder implements View.OnClickListener {

    public ViewHolder(View itemView) {
        super(itemView);
        itemView.setOnClickListener(this);
    }

    @Override
    public void onClick(View v) {
        // Below line is just like a safety check, because sometimes holder could be null,
        // in that case, getAdapterPosition() will return RecyclerView.NO_POSITION
        if (getAdapterPosition() == RecyclerView.NO_POSITION) return;

        // Updating old as well as new positions
        notifyItemChanged(selected_position);
        selected_position = getAdapterPosition();
        notifyItemChanged(selected_position);

        // Do your another stuff for your onClick
    }
}

hope this'll help.