Could someone explain a couple of scenarios where the system design can justify the use of an encryption solution, respectively, as 3DES and Blowfish?
I'll add a few, one related to the backwards compatability: if you have a hardware implementation that only does 3DES (many older smartcards) then 3DES could be preferred over AES. Hardware accelerators can be used for both speedups and security (side channel attacks, see below).
3DES implementations may be less vulnerable to side channel attacks (although it certainly is not immune from it). AES is harder to get right - as I've come to understand - because of it's internal design (table accesses). AES better algo, bigger blocksize or key size does not mean much when confronted with a good side channel attack.
3DES has a 8 byte blocksize compared with 16 bytes for AES which can lead to a bit more overhead when using it in block mode encryption. Of course, this one can be mitigated by using a stream mode cipher, and we're only talking about a few bytes for the last block. This is an extremely thin argument for this reason.
I'll be a bit shorter on Blowfish: variable key size and sometimes faster than AES, less likely to be implemented in hardware, but backwards compatibility may be reasons, and the 8 byte blocksize again.
None of the three reasons above is generally enough to choose 3DES or Blowfish over AES of course.