Although I maintain a virtually unknown personal blog about videogames, I like the idea of writing blog-style content that can reach a wider, more general audience. Recently a Facebook friend of mine started blogging for huffingtonpost.com which seems to be pretty open to submissions as long as they're well written and interesting. Are there any other really big blogs where I could have a chance in submitting something?
If you have a look around almost all technology sites welcome submissions. Many will let you pitch an idea first, and some will ask for you to submit a finished article for them to review.
Either way, just have a look around sites you are interested in, look for an email address, and pitch an idea. The worst answer you can get is a no, and if you've got some interesting ideas, they are more than likely to get picked up.
I've been an on-again, off-again writer for Ars Technica for nearly ten years. (Mostly off for the last four.) Periodically, they solicit submissions from new writers, usually in a few specific subject areas. I don't know that video games is one of them, because Ben, Casey, and Andrew seem to have that on lockdown both in terms of volume and quality.
And yes, they pay, because they believe that good writing (and journalism) deserves to be compensated. The EIC (Ken) is a stand-up guy, and really cares about his people. The ME (Eric) is really great, too. If you want to cut your teeth doing online journalism, I can't think of a better group to learn with.
If you think you want to write about video games, you should drop Ben an email. He's the gaming editor, and he can tell you more. (Even if it's a no.)