Show/hide widgets in Flutter programmatically

Invisible: The widget takes physical space on the screen but not visible to user.

Gone: The widget doesn't take any physical space and is completely gone.

---

Invisible example

Visibility(
  child: Text("Invisible"),
  maintainSize: true, 
  maintainAnimation: true,
  maintainState: true,
  visible: false, 
),

Gone example

Visibility(
  child: Text("Gone"),
  visible: false,
),

---

Alternatively, you can use if condition for both invisible and gone.

Column(
  children: <Widget>[
    if (show) Text("This can be visible/not depending on condition"),
    Text("This is always visible"),
  ],
) 

UPDATE: Since this answer was written, Visibility was introduced and provides the best solution to this problem.

---

You can use Opacity with an opacity: of 0.0 to draw make an element hidden but still occupy space.

To make it not occupy space, replace it with an empty Container().

EDIT: To wrap it in an Opacity object, do the following:

            new Opacity(opacity: 0.0, child: new Padding(
              padding: const EdgeInsets.only(
                left: 16.0,
              ),
              child: new Icon(pencil, color: CupertinoColors.activeBlue),
            ))

Google Developers quick tutorial on Opacity: https://youtu.be/9hltevOHQBw

To collaborate with the question and show an example of replacing it with an empty Container().

Here's the example below:

import "package:flutter/material.dart";

void main() {
  runApp(new ControlleApp());
}

class ControlleApp extends StatelessWidget { 
  @override
  Widget build(BuildContext context) {
    return new MaterialApp(
      title: "My App",
      home: new HomePage(),
    );
  }
}

class HomePage extends StatefulWidget {
  @override
  HomePageState createState() => new HomePageState();
}

class HomePageState extends State<HomePage> {
  bool visibilityTag = false;
  bool visibilityObs = false;

  void _changed(bool visibility, String field) {
    setState(() {
      if (field == "tag"){
        visibilityTag = visibility;
      }
      if (field == "obs"){
        visibilityObs = visibility;
      }
    });
  }

  @override
  Widget build(BuildContext context){
    return new Scaffold(
      appBar: new AppBar(backgroundColor: new Color(0xFF26C6DA)),
      body: new ListView(
        children: <Widget>[
          new Container(
            margin: new EdgeInsets.all(20.0),
            child: new FlutterLogo(size: 100.0, colors: Colors.blue),
          ),
          new Container(
            margin: new EdgeInsets.only(left: 16.0, right: 16.0),
            child: new Column(
              children: <Widget>[
                visibilityObs ? new Row(
                  crossAxisAlignment: CrossAxisAlignment.end,
                  children: <Widget>[
                    new Expanded(
                      flex: 11,
                      child: new TextField(
                        maxLines: 1,
                        style: Theme.of(context).textTheme.title,
                        decoration: new InputDecoration(
                          labelText: "Observation",
                          isDense: true
                        ),
                      ),
                    ),
                    new Expanded(
                      flex: 1,
                      child: new IconButton(
                        color: Colors.grey[400],
                        icon: const Icon(Icons.cancel, size: 22.0,),
                        onPressed: () {
                          _changed(false, "obs");
                        },
                      ),
                    ),
                  ],
                ) : new Container(),

                visibilityTag ? new Row(
                  crossAxisAlignment: CrossAxisAlignment.end,
                  children: <Widget>[
                    new Expanded(
                      flex: 11,
                      child: new TextField(
                        maxLines: 1,
                        style: Theme.of(context).textTheme.title,
                        decoration: new InputDecoration(
                          labelText: "Tags",
                          isDense: true
                        ),
                      ),
                    ),
                    new Expanded(
                      flex: 1,
                      child: new IconButton(
                        color: Colors.grey[400],
                        icon: const Icon(Icons.cancel, size: 22.0,),
                        onPressed: () {
                          _changed(false, "tag");
                        },
                      ),
                    ),
                  ],
                ) : new Container(),
              ],
            )
          ),
          new Row(
            mainAxisAlignment: MainAxisAlignment.center,
            children: <Widget>[
              new InkWell(
                onTap: () {
                  visibilityObs ? null : _changed(true, "obs");
                },
                child: new Container(
                  margin: new EdgeInsets.only(top: 16.0),
                  child: new Column(
                    children: <Widget>[
                      new Icon(Icons.comment, color: visibilityObs ? Colors.grey[400] : Colors.grey[600]),
                      new Container(
                        margin: const EdgeInsets.only(top: 8.0),
                        child: new Text(
                          "Observation",
                          style: new TextStyle(
                            fontSize: 12.0,
                            fontWeight: FontWeight.w400,
                            color: visibilityObs ? Colors.grey[400] : Colors.grey[600],
                          ),
                        ),
                      ),
                    ],
                  ),
                )
              ),
              new SizedBox(width: 24.0),
              new InkWell(
                onTap: () {
                  visibilityTag ? null : _changed(true, "tag");
                },
                child: new Container(
                  margin: new EdgeInsets.only(top: 16.0),
                  child: new Column(
                    children: <Widget>[
                      new Icon(Icons.local_offer, color: visibilityTag ? Colors.grey[400] : Colors.grey[600]),
                      new Container(
                        margin: const EdgeInsets.only(top: 8.0),
                        child: new Text(
                          "Tags",
                          style: new TextStyle(
                            fontSize: 12.0,
                            fontWeight: FontWeight.w400,
                            color: visibilityTag ? Colors.grey[400] : Colors.grey[600],
                          ),
                        ),
                      ),
                    ],
                  ),
                )
              ),
            ],
          )                    
        ],
      )
    );
  }
}