Ok, the same goes for the monitor I currently have. It's old, but still works, but it has a perfectly square screen. Should I get a new one?
Up to you really... If you have the budget to spend, then a 23" / 24" monitor can be had for around $150, but if you aren't having any problems with the old 4:3 monitor then stick with it. Again, no need to spend the money if you are happy with what you have.
Acer 23" LED Backlight LCD ($150 => http://www.microcenter.com/single_product_results.phtml?product_id=0354785