One thing that I've seen people question time & time again is the question of "is a custom domain really necessary?". I'll be the first to admit that I only used the .blogspot.com URL for a short amount of time before I transferred to a custom .com domain, even without knowing the full benefits. If you are in the same boat I was a few years back or even just contemplating the idea, here's my thoughts.
IT GAINS TRUST Personally, I'm more likely to click through a link that has a custom domain than a regular one as it gains more trust. Custom domains usually demonstrate a level of serious-ness, which then gains the trust of your audience.
IT LOOKS PROFESSIONAL As I mentioned in the point above, custom domains demonstrate a level of serious-ness. If you're looking to use your blog as a serious career path or just a serious hobby then I'd say it's definitely worth the leap.
IT'S EASIER FOR YOUR READERS In a non-offensive way, readers are selfish. People will only click on your links if you're giving them something nobody else has, whether that be new tips or just your writing style. Changing your URL to something shorter and snappier will appeal to their lazy side!
IT COSTS This is more of a minor disadvantage but still one I wanted to include. Depending on what kind of domain you're looking for, prices can range from £4 to £500+ per year. You can check the different prices for your own custom domain using GoDaddy's domain search.
IT CAN BE HARD TO SET UP 2 years ago when I set up my .com domain, I had a nightmare installing it as I had very little knowledge of how the behind-the-scenes of a website worked. Now I know a little bit more it's not too difficult, but you could always pay somebody to install it for you.
Overall I'd definitely recommend taking the leap into a custom domain if you're serious about your blog. Although it can be pricey and difficult to set up, you'll soon start to reap in the benefits!