I use Google fonts quite a lot, especially ones like:-
<link href='http://fonts.googleapis.com/css?family=Titillium+Web:200' rel='stylesheet' type='text/css' />
Should these only be used for 'parts' of the web site or is it okay to use these for the content of the entire site?
body {
background-color:#292828;
font-family: 'Titillium Web',Arial, Helvetica, sans-serif;
}
Also, is there any alternative/better ways to use custom fonts other than using Google fonts or images?
You can create your own webfonts, if you want.
There's webfont generators, and here's one.
And about your question about are google webfonts reliable?
Yes. Yes they're. Think it like this: When did Google go down? If it happens, it's probably the last thing you should care of.