As of 2016, approximately 50% of the time people look at your website they are viewing it on a mobile device (e.g. iPhone or another smartphone, iPad or another tablet, etc.).
Does your site look good on a mobile device? If it’s an older site (say, 2012 or earlier), chances are it doesn’t, as it wasn’t the norm to take that into account when developing web sites at the time. Nowadays, responsive websites aren’t just a luxury–they’re a necessity.
Now, you could break out a bunch of different devices that you have around the house/office and see how your site looks on each one, but there’s a better way. We suggest that you check out the Google resizer tool.
So, how does it look? If there are any weird formatting issues, or if it just looks plain “bad”, you may want to think about updating your web site.