I designed mine myself, but, I was actually trained as a designer.
You don't have to be a designer anymore to make a decent web page. HTML is pretty easy to learn and there are a lot of editing programs out there that will do it all for you if you don't want to take the time to learn HTML. That being said, if you're not a designer and can put up the money to hire one, you may as well do it because no matter how good those editing programs are, they are no substitute for someone with actual training in design and user-interface.
I design my own sites for the most part. The only time I will use someone else's design for certain parts of it is when I buy a Wordpress plugin, such as Ubermenu. Granted I can still customize the appearance of it, but it's a huge timesaver vs. trying to code the whole drop down menu manually each time.
Depending on the kind of design I have in mind, if it's something too complex I'll outsource it to a freelancer or reputable design company, but if it's simple I'll often do it myself in a program like Illustrator and touch it up in Photoshop. Also, if the project will take more than a few hours, I'll save a lot of time outsourcing it to experienced artists so I can use that time to focus on creating content.
I use wordpress themes and pay for custom logos/header graphics as needed. There are so many talented people out there offering their services at decent price -- it's just too good to pass up -- especially if you're like me and have no graphic skills to speak of.
Every website I create or own, I always make a custom style for it, just to make it stand out, I have never paid someone to do it for me, but I have worked with other people for fun. I use Photoshop and Notepad ++
This is a website development site so I think you will find that most people design their sites themselves however in some cases it makes sense to hire someone instead. For example, many times a client may be on a tight budget and modifying a pre made theme makes more sense than designing and coding something from scratch.
I had to hire a designer because I had no idea what I was doing. I needed it set up urgently and there was no time for me to learn. Now I now my stuff and I can even set up websites for others. It's really an advantage when you know how to design it on your own.