You have decided that you really like Dropbox (my review) but realize that 2gb is not going to be enough storage for you. You also do not want to have to pay for an upgraded plan. Fear not; you can get almost 20gb worth of free space by following a few steps.
Sign up for Dropbox from a referral. Signing up through a referral will start your free account off with 2.25gb (and extra 250mb) instead of the normal 2gb. To do that click on this link and sign up on the screen you are brought to. Your extra 250mb will be credited to your account once you install Dropbox on your computer.
If you have already signed up, and did so without using a referral, you can either forgo the 250mb bonus or uninstall Dropbox and use a different email address to sign up from a referral. Generally speaking, once you have installed Dropbox on your computer (or if you have gotten any referral bonuses yourself [more on that in step 4]) you probobly do not want to go through the hassle involved to get the starting bonus; obviously your call though.
Log on to your account and head to the Get Started tab. There are six 'quests' which are more like tutorials. It would be a good idea to go through them just to get familiar with the service even if there was no extra free space involved. Fortunately for the free space hogs in us all there is. Once you complete the quests you will get an extra 250mb of free space to your Dropbox account.
Log on to your account and head to Dropbox.com/free. From there you can:
Connect your Twitter account with Dropbox -> +128mb
Connect your Facebook account with Dropbox -> +128mb
Follow Dropbox on Twitter -> +128mb
Send Dropbox short feedback message -> +128mb
Tweet the feedback that you sent to Dropbox -> +128mb
Post the feedback you sent to Dropbox on your Facebook Wall -> +128mb
If you complete each step you will net an additional 768mb of free space to your Dropbox account even if you delete the message, unfollow, or disconnect your account later.
Log on to your account and head to the referral page. From there you can invite your friends/colleagues/family to Dropbox. You get an additional 250mb of free space for each person you refer who then signs up and installs Dropbox on their computer. There is a limit of 32 referral credits for extra space for a total of an additional 8gbs of free storage too your Dropbox account. Referring more can not hurt in case Dropbox decides to up that limit as they have in the past.
If you have a .edu email address from school/college, log on to your account and head to Dropbox.com/edu. Once there register your .edu email address. Once the address is verified the referral bonus is doubled from 250mb to 500mb. The limit of 32 referral credits remains, but instead of maxing out at an additional 8gb you can get a maximum of 16gbs of additional space to your Dropbox account. The doubling of the referral bonus with your .edu email address is retroactive.
If you max out on all the possible standard free space your Dropbox account would have: 2gb (starting) + 250mb (sign up from referral bonus) + 250mb (get started quests) + 768mb (linking accounts / free page) + 16gb (max referral of others with a .edu email) = 19.268gb of free space.
The reason I said standard free space is because every so often Dropbox launches a temporary promotion where users can earn more free space.