Even though there are some workarounds it's strongly not recommended, because either of these services were designed to handle that. Also if it's used to get some extra quota it's against Dropbox's ToS and I'm pretty sure that it is against the Ubuntu One's as well.
Here is what a Dropbox dude (N.N.) said on this matter:
Note that in the vast majority of cases where people are asking about multiple accounts is best solved by Shared Folders. Unless there are two different people using the same computer, which different OS accounts is the proper way of handling it.
Third party applications and hacks that are designed to get multiple Dropbox instances running at the same time for one user is not recommended, not only because they are completely unsupported (by the Dropbox team at least), but also because Dropbox is not meant to be utilized in such a manner. So the chance of issues is a lot higher than running Dropbox as per normal.
PS: Also, please keep in mind that using multiple Dropbox accounts to circumvent our quota limitations is against our ToS.