Building your own website gives you a 'home base' to showcase your images and share details about what your work. Social media platforms give you that ability too of course, but with more limitations. Your own site gives you more control, lets you make the design decisions, and makes you less vulnerable to the latest whims of Facebook or Google+.
It's not easy to choose the right platform though and I spent a lot of time looking and trying out a few options when I was first building this site. A key question to start is how you want to use the site. Is it primarily to showcase your images? Do you want to be able to sell prints online? Will you be blogging?
With these considerations in mind, these are the options I recommend checking out.
Traditionally a blogging platform, Wordpress is a powerful system that is public domain. This means that anyone can contribute to the system rather than it being in the hands of one company. Using Wordpress will give you the most control over your site beyond programming it yourself or hiring a specialist contractor to do so. It will also take the most time to get right though. You'll need a hosting platform (i.e. where your site will be stored), and you may find you want to pay for a 'premium theme' and plugins to help display your photos. It's used by many large companies and is the most common platform in use today.
Based on the same development platform as Wordpress.org, Wordpress.com incorporates hosting facilities too so you don't have to find and purchase that separately. There is even a free version, although you're likely to find adverts appearing on your site if you choose that option. You give up some of the flexibility of Wordpress.org in exchange for the convenience of an all-in-one package.
Tumblr is a free, well presented and very popular visual blogging platform. It's much closer in nature to a social media platform but if you don't need a full website or portfolio showcase then Tumblr is very quick and easy to set up. You are restricted to showing images within a blog format though.
500px has similarities to Flickr in being primarily a photo hosting site that incorporates social elements and lets you showcase your images. You could think of 500px as a portfolio site. A lot of thought has gone into making the images look as good as possible, and the general standard of photos on the site is impressive although they also tend to be of certain styles such as high detail, HDR and macro shots. If you want a truly bespoke site, you need to look elsewhere. But if you just want to show great photos and have the option to sell some prints, 500px could be a good choice.
When I was comparing Zenfolio directly with SmugMug they seemed very similar in terms of flexibility and features. At the time (2013), I much preferred the interface design of SmugMug. It just seemed more intuitive to use. Making the same decision today, I might be more swayed by Zenfolio's blogging features.
I used Weebly for a while to host a magazine-style site. It's easy to get started and very easy to use with a simple and intuitive interface. It also has good blogging features. There is a free version with no adverts, although you the eCommerce options are only available on paid subscriptions. I've only used the basic account so far but from what I've seen I rate it very highly.
SmugMug, Zenfolio and Squarespace are probably closest competitors to each other. They each enable you to design and quickly construct a new site using their templates. They offer features such as galleries and slideshows that make it easy to show a series of photos.
SmugMug underwent a major update in 2013 and now has the most modern interface. It's feature set is good, with excellent gallery tools and a wide range of print services built in. The brand has gained a lot of support and is being pushed further with marketing initiatives such as the excellent SmugMug Films channel on YouTube. The only downside for me, and the reason I moved my site away from SmugMug, is the lack of blogging facilities.
Squarespace is likely to be a good option for most people at the moment. It may not be quite as flexible as a self-hosted Wordpress site, but you'll spend a loss less time fixing things and hopefully a lot more time on your photography. It has an intuitive interface that is easy to learn, but does allow you to add CSS code if you're not entirely happy with the provided templates. Blogging options are good and you can export your blog content as a back-up or if you decide to migrate it in the future. This site is build on Squarespace and I've been impressed with that they offer.
There are others options too but these are ones I'm most familiar with. If you have other recommendations please do let me know. I'll talk more about Squarespace specifically and how to get started with it in a future post.