jsFiddle Demo

jQuery provides several selectors (full list) in order to make the queries you are looking for work. To address your question "In other cases is it possible to use other selectors like "contains, less than, greater than, etc..."." you can also use contains, starts with, and ends with to look at these html5 data attributes. See the full list above in order to see all of your options.

The basic querying has been covered above, and using John Hartsock's answer is going to be the best bet to either get every data-company element, or to get every one except Microsoft (or any other version of :not).

In order to expand this to the other points you are looking for, we can use several meta selectors. First, if you are going to do multiple queries, it is nice to cache the parent selection.

var group = $('ul[data-group="Companies"]');

Next, we can look for companies in this set who start with G

var google = $('[data-company^="G"]',group);//google

Or perhaps companies which contain the word soft

var microsoft = $('[data-company*="soft"]',group);//microsoft

It is also possible to get elements whose data attribute's ending matches

var facebook = $('[data-company$="book"]',group);//facebook

//stored selector
var group = $('ul[data-group="Companies"]');

//data-company starts with G
var google = $('[data-company^="G"]',group).css('color','green');

//data-company contains soft
var microsoft = $('[data-company*="soft"]',group).css('color','blue');

//data-company ends with book
var facebook = $('[data-company$="book"]',group).css('color','pink');

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<ul data-group="Companies">
  <li data-company="Microsoft">Microsoft</li>
  <li data-company="Google">Google</li>
  <li data-company ="Facebook">Facebook</li>
</ul>

jsFiddle Demo

jQuery provides several selectors (full list) in order to make the queries you are looking for work. To address your question "In other cases is it possible to use other selectors like "contains, less than, greater than, etc..."." you can also use contains, starts with, and ends with to look at these html5 data attributes. See the full list above in order to see all of your options.

The basic querying has been covered above, and using John Hartsock's answer is going to be the best bet to either get every data-company element, or to get every one except Microsoft (or any other version of :not).

In order to expand this to the other points you are looking for, we can use several meta selectors. First, if you are going to do multiple queries, it is nice to cache the parent selection.

var group = $('ul[data-group="Companies"]');

Next, we can look for companies in this set who start with G

var google = $('[data-company^="G"]',group);//google

Or perhaps companies which contain the word soft

var microsoft = $('[data-company*="soft"]',group);//microsoft

It is also possible to get elements whose data attribute's ending matches

var facebook = $('[data-company$="book"]',group);//facebook

//stored selector
var group = $('ul[data-group="Companies"]');

//data-company starts with G
var google = $('[data-company^="G"]',group).css('color','green');

//data-company contains soft
var microsoft = $('[data-company*="soft"]',group).css('color','blue');

//data-company ends with book
var facebook = $('[data-company$="book"]',group).css('color','pink');

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<ul data-group="Companies">
  <li data-company="Microsoft">Microsoft</li>
  <li data-company="Google">Google</li>
  <li data-company ="Facebook">Facebook</li>
</ul>