There is no valid reason for storing plain text passwords. Every time someone says "but we want it because we need to X" there is a better way to achieve X (or Y, where Y has the same effect as X in the end) that does not require plain text password storage (but may require a little extra coding+testing).
If anyone who says that the "but may require a little extra coding+testing" constitutes a valid reason, then they should not be trusted with any of your data. It is like leaving the office door unlocked because you couldn't be bothered to fish your keys out of your pocket and find the right key. It is an excuse (a pathetic excuse) for plain text passwords, but it is not a valid/good/acceptable reason.
Of course there are probably a great many sites that are unprofessionally constructed (in the auth credentials storage area at least) and you may never know until something goes wrong, so for safety you should not use the same password for multiple sites (keepass and similar utilities make keeping track of multiple password easy enough) then at least if one site is hacked the perp only gets access to that one site as you rather than potentially many sites.