Dropbox client does not allow you to run multiple instances concurrently but you can get around with this issue by running it as different Windows User Accounts. With a little help of Dropboxen by Dale H, you can easily run multiple instances of Dropbox client concurrently.

Get a copy of Dropboxen here if you haven't. You need to unzip the files into your Dropbox installation folder. The default installation folder is C:\Users\[Your User Name]\AppData\Roaming\Dropbox\bin\ or C:\Program Files\Dropbox\ depending on your OS.

You will need to edit the file Dropboxen.xml but before doing that, you need to create a Windows User Account for each Dropbox account that you will be using (it has to be an Administrator account, not Standard User). For Windows XP, go to Control Panel > User Account > Create a new account, remember to set a password for your account. For Windows Vista or 7, go to Control Panel > User Accounts and Family Safety > Add or remove user accounts, remember to set a password for your account. You will need to login to your new account and install Dropbox client, do this for every single User account. After you're done with creating User Accounts and installations, log off and switch back to your main account. Let's edit Dropboxen.xml, you can open it with any text-editor:

Dropboxen.xml:

<?xml version="1.0"?>
<root>
<accounts>
<account username="(windows user account name)" password="(windows user account password)" />
<account username="(windows user account name 2)" password="(windows user account password 2)" />
</accounts>
</root>

Now you need to fill in your user accounts and passwords. This is what my Dropboxen.xml looks like:

<?xml version="1.0"?>
<root>
<accounts>
<account username="TinoTK" password="somepassword" />
<account username="Dropbox1" password="pass1" />
<account username="Dropbox2" password="pass2" />
</accounts>
</root>

Now go ahead and click on Dropboxen.exe to start Dropbox client again, there should be multiple instances of Dropbox client according to how many accounts you put in Dropboxen.xml. Now you can use multiple Dropbox accounts at the same time. The last thing you need to do is create a shortcut for Dropboxen.exe in your Startup folder.