In the past, popular system-standard fonts have been called "web-safe" fonts. It has been considered good practice by many in web design to stick to these. Why, do you ask? During the early days of the Internet, there wasn't really a standard font that one use that rendered across all the different platforms. However, there were fonts more likely to be a person's computer, like Arial, Helvetica, and Times New Roman.
But nowadays, things are a bit different. With modern browsers, it's now safe to use "web fonts," which a technique using a remote font file to render a specific font on a web page using @font-face, which give more creative freedom and flexibility when designing a web page. This is by no means a new concept, there has been at least partial support for it going back until at least IE 5.5.
@font-face has been formally included in the most recent version of W3C's CSS standards (CSS3, it was taken out of CSS2.1). The Google Fonts API offers a fast an easy way to render the fonts in their library instantly usable, by generating the code you need after picking the font you like.
@import url(http://fonts.googleapis.com/css?family=Open+Sans);
body { font-family: 'Open Sans'; }
But that doesn't mean you can go wild with your web font choices. You should take steps to use a CSS font stack, to ensure that you gracefully degrade your text experience in case your chosen does not load.
body {font-family: "Open Sans", "Arial", "Helvetica", sans-serif; }
A CSS font stack should includes similar web-safe fonts, with the last declaration in the stack being a generic font family ("serif" or "san-serif"). What happens is if you browser can't find one font, it looks for the next one down the line.
But why is this important? After all using web-safe fonts and CSS font stacks seems dated especially since @font-face has great support across all the modern browsers.
There's a couple of reasons... one of them being the completeness of these fonts. Certain characters in your font chosen font might not available (this font lacks the ™ character.), when that happens, the browser will attempt to render the unavailable characters using the next font in your CSS font stack. If you don't have such a font stack, the browser's use your default standard font (you can set this is you browser settings). Why would this ever be a problem? Lets say you have a serif headline (like Times New Roman) in the aforementioned font and you browser default font is a san-serif font (like Arial). The mismatch between the two different style might not necessarily look good. You have no control of what a should have their default browser font, nor should you try to.
Another reason would be the internet itself. On occasion people internet goes down and so to the services on the Internet. These fonts you have are hosted on the internet. If the service hosting it does down, even it it's the best font in the world, it won't ever load, instead it'll use your browser's default standard -- unless you specify a web-safe font in your CSS font stack. I website can look drastically different if all of a sudden your intended font file isn't available, due to some sort of service interruption.
You can disable the downloading of web fonts client side via your browser. But why would you ever want to do this? This One of the most overlooked reason, performance. This is more desirable for users who have slow Internet connections for one reason or another. In most cases the way to do this on a browser is somewhat obfuscated. It might take 1.2 more seconds to load a font from Google's Font API, when the page would normally load in .011 seconds. While we take speed for granted, since fast broadband is readily available in most developed countries, it's important to ensure the visibility and consistency of your site's typography is not impacted to to the restriction of the user (accessibility option) or their platform (bandwidth, browser).
So in closing, what I'm trying to say is that, it's alright to use fonts that are not web-safe to make things look nice, but don't go all crazy and be reliant on them as not all users experiences are created equal (browsers my render fonts an default sizes differently depending on the browser and/or system setting, e.g., ClearType). You can't really tell a user how to use your site, but you can tell them how they can get the best experience. If they're unable to follow through may sure you adjust things accordingly so that they can still have a good experience. Things on the web aren't necessarily set in stone (or on ink and paper). The variable flexibility of the Internet lets users serve up content in a way that's most comfortable to them.