If you don't already use Dropbox you really should. It's like having a USB drive on the Internet that you can use to share files between all your different computers and smartphones. You can also use it to share files with other people remotely. It's also a great way to backup your most important files, like source code or crucial documents, and that's the main thing I use my account for. By default free accounts will get just 2GB of storage space, and while you can pay a monthly fee for more space there are a few ways you can get a bunch of extra space for free. My account is over 24GB, all for free.
The first thing and most obvious thing to do to get more Dropbox space is to go through the step by step "Getting Started" list on the Dropbox site. This includes hooking up Dropbox to your Facebook and Twitter accounts, which I was a bit hesitant to do at first but haven't had any complaints about doing since.
The current beta software release on the Dropbox forums will net you 5GB of bonus space if you use the import media feature during the beta. They recommend you backup the contents of your Dropbox account before messing with the beta software, which is a good idea. You can't just drag and drop media files into your Dropbox folder to get the extra space, you have to actually upload 5GB worth of images or videos off an external drive using the Dropbox option that comes up with autorun when you plug the removable drive in. I don't know how long this beta bonus will be given out for, so I recommend jumping on this while you can.
I installed the beta on my Windows 7 partition and plugged in an SD card from my camera and the autorun feature popped up asking what I wanted to do with the SD card. The Dropbox import option was towards the top of the list. If you've disabled autorun for removable storage you'll want to turn it back on for this. Since I had less than 5GB of media on the SD card I also uploaded some media files off a thumb drive using the import feature to max out the 5GB bonus.
The Dropbox referral system can get you a lot of bonus free space, as a reward for getting new users to sign up for Dropbox and install the software. If you connect a .edu email account to your Dropbox account you'll double the max space you can get from referrals from 8GB to 16GB, and double the space you get from each referral from 250MB to 500MB. Bonus space you've already gotten from referrals will increase even if you add the .edu email account later. You'll need to convince 32 people to sign up for Dropbox using your referral link AND install the software on their computers to max out your account, any more than that won't get you anything. I was only able to convince one person I know to bother using my referral link to open their Dropbox account, but then I read about a much more effective approach than simply asking people you know.
I first read about people using Google Adwords to share their Dropbox referral links on Lifehacker, who posted a short blurb about it and linked to a blog where someone had done this. A while later Lifehacker posted their own guide to doing this, with a few more tips and suggestions and lot of useful comments from readers. It's well worth going through and reading all of that to minimize the amount you spend on Adwords. Normally this would cost you, but you can get Adwords coupons from Google and from web hosting companies for opening accounts. Since I had gotten a $100 Adwords coupon code doing this cost me nothing, just a little over $16 of the $100 credited to my account, leaving me with plenty to play with Adwords later on for other uses. Reading the step by step instructions on Lifehacker was a great introduction to using Adwords, something I'd been meaning to learn more about anyway.
There have been a few people who've been suspended from Google Adwords after running these Dropbox ads, so this may not be the best thing to try if you depend on your Adwords account for a living. Google's customer support for Adwords seems to have a poor reputation online, with many people complaining of suspensions without reasons or explanations from Google. Just make sure your ads are not spammy or obnoxious or make false claims or do anything that would fall afoul of the Google Adwords terms of service, that all should go without saying.
The last way to get free Dropbox space is to keep your eyes open for temporary opportunities, like the current media upload beta and the scavenger hunt promotion that Dropbox had some time ago. The scavenger hunt got me a bunch of extra space with very little effort on my part, since other brighter people had gone and done the work of solving the puzzles and shared their findings online. I wouldn't be surprised to see more promotions over time, since it apparently costs so little for Dropbox to provide space to most people, since most people don't use all the space available to them and the paid accounts more than subsidise the free accounts.
There are a bunch of uses for all this extra space besides just backups of files on your computer and one of the most interesting to me is automatic website backups. Wordpress sites can use a simple plugin called Wordpress Backup to Dropbox to make automatic nightly backups of the entire site to a Dropbox account. This is a great way to guard against problems with cheap web hosts that have security failures or just randomly delete your files all of a sudden. That's actually happened to me.