Today, early 2019, there are many, many brands out there that sell sets with Lego-compatible pieces. Most of them are Chinese brands, but there's also several brands from other countries.
Here's but some of this long list of brands :
Lepin is a brand specialized in cloning complete Lego sets, from individual pieces & minifigs to instructions and box art. That means this brand is véry controversial and buying it may be illegal in your country. The quality of the bricks is very good, though, although Lepin sets are more likely to have missing bricks or poorly moulded bricks than Lego sets.
All other brands listed sell their own sets with their own unique designs. The quality & price varies significantly from brand to brand. Many of these brands produce real-life military designs (tanks, airplanes) that Lego has a policy of never releasing.
In my experience, Oxford provides the highest quality, and in fact may even provide better quality than Lego in some aspects. However, it's also at a similar price range as Lego and not a good option if cost is a primary criterion for looking at other brands. Kre-O bricks come from Oxford but are marketed by Hasbro and are easier and cheaper to find on Amazon.
XingBao also provides high quality sets, including some modular buildings with piece counts > 4,000. And while not without flaws, the designs of these modular buildings is on par with those sold by Lego, at a fraction of the cost. Xingbao even has a version of the Lego Ideas system where people vote for uploaded sets they want to see put into mass production. XingBao has the same mother company as Lepin, however, sort of a "legal" branch of the same company. So you may want to avoid it if you have a problem with Lepin's business practices.
For a brand that is almost as high quality as XingBao but which isn't shrouded in the same controversy, you might want to check out Enlighten. Especially their recent sets are pretty high quality. They don't sell any sets as complex as full-size modular buildings, though.
Where can you buy these brands, you might want to know? For non-Chinese brands like Oxford or Cobi, you might want to check out Ebay or Amazon. For Chinese brands, the most popular venue is AliExpress.