Why is select by drawing a rectangle not working in ArcMap?

wild stab in the dark, but if you're using QGIS you need to ensure that the layer containing the points is highlighted in the layers list for the selection to work.

Same I believe goes for ArcGIS (i.e. the layer needs to be highlighted in Table of Contents).

In MapInfo you need to check that the layer is 'selectable' in layer control, and be aware that MapInfo will drill down through the layers in your workspace (top down) until it finds something that it can select, therefore if a layer located higher in the layer control is selected, the selection will not get down to your point layer.

Also I common mistake I have made is not having the layer set as a selectable layer in ArcGIS. An easy fix for this is to right click on the layer in the Table Of Contents, chose "Selection", and then select "Make This The Only Selectable Layer".

A better way to go would be to enable the the "Set Selectable Layers" tool somewhere in the customize menu. Unfortunately i don't have ArcGIS in from of me an can't walk you through the steps at the moment.

In ArcGIS 10.0 and above, the 4th icon from the left at the top of the Table of Contents pane is where you can toggle off/on whether layers are selectable or not. You can also use Hyperion's suggestion of setting points to be the only selectable layer. I've never seen where the layer has to be highlighted in the TOC, but maybe that's a version of Arc I haven't worked with.

I am using ArcGIS 10.2 and was also not able to select features.

I was able to select features again by going to "selection" tab> "Interactive Selection Method" > check "Create New Selection"

If the "Select from Current Selection" choice is checked and there are no features currently selected then the select features tool will not be able to do anything. This was my problem.

I had similar problem. Could not select from the select feature, and clear selected feature stays gray. So my layer was not yet projected.

To correct this click on the layer, then Data, then Export data, then OK. Then from the newly created layer you can select features.

I ran into this before as well. What I had done is changed the 'Interactive Selection Method' to 'Remove From Current Selection,' so every time I tried to select something, I was actually deselecting nothing!

Try this:

1. Table of Contents | Right-click layer | Selection | Make this The Only Selectable Layer

2. Selection (from ribbon) | Interactive Selection Method | Create New Selection

This should do it for you.