How secure is an encrypted wallet? Would you store an encrypted wallet (backup) of significant value on dropbox?

Assuming the passcode is good and secure.

The wallet in question is bitcoin-qt, encrypted using the built-in encryption feature.
Yes, you could store encrypted wallet in the dropbox.
From the first glance into the source code, the encryption algorithm is AES 256 CBC. This is industry standard protocol that is NOT known to be brute-force crackable* (subject to correct usage). You can read up more on the B. Schneier blog AES tag, where the most recent post say

[...] Reading the above, the obvious question to ask is: can the NSA
break AES?
My guess is that they can't. That is, they don't have a
cryptanalytic attack against the AES algorithm that allows them to
recover a key from known or chosen ciphertext with a reasonable time
and memory complexity. I believe that what the &quot;top official&quot; was
referring to is attacks that focus on the implementation and bypass
the encryption algorithm: side-channel attacks, attacks against the
key generation systems (either exploiting bad random number generators
or sloppy password creation habits), attacks that target the endpoints
of the communication system and not the wire, attacks that exploit key
leakage, attacks against buggy implementations of the algorithm, and
so on. These attacks are likely to be much more effective against
computer encryption.

There are chances, that the satellite code around the algorithm wasn't used correctly, or that there is a back door. There are some talks on the general security concepts in this thread. Despite it being open-source, there is no guarantee there are no bugs.
As an alternative you can store your wallet on the encrypted TrueCrypt partition. TrueCrypt source code is currently being investigated by the independent body for the security flaws.
Personally, I would use default encryption and trust it provides sufficient level of protection. Make sure your pass-phrase is strong, long and random, and that it is stored securely.