For a bit of perspective, classful network types are still used as a common terminology for internal and private (RFC1918) networks.
It's true that since BPG4, CIDR has made classful Internet boundaries meaningless, but when talking about interior networks and classful routing protocols, it's still useful to know the differences in the classes.
To answer your question, classful boundaries are fixed in size. The subnet masks for each are as follows:
CLASS A: 255.0.0.0 (/8)
CLASS B: 255.255.0.0 (/16)
CLASS C: 255.255.255.0 (/24)
CLASS D: N/A (These are used for multicast traffic and are routed internally using PIM or DVMRP and do not correspond to traditional subnet masks)
CLASS E: N/A (There are experimental and/or reserved addresses)
A larger collection of classful networks is called a supernet and a sub-divided classful network is called a subnet. When you talk about the largest possible subnet mask, you are generally referring to the largest possible network portion and smallest usable host portion. For routing subnet purposes, the largest subnet mask is 255.255.255.252 (/30). This is typically used for point-to-point links and transit networks that only need two hosts/gateways on a subnet.
There is no limit to the maximum size a supernet can be, up to a subnet mask of 0.0.0.0 (/0), which would indicate that every address is local and not routed. Note that this is different than a default route of 0.0.0.0, which is the least specific route and routes all traffic not defined by a more specific route.
If you are looking for the largest possible subnet mask to define all Class A networks and so on, here is the list based upon the first octet:
CLASS A: 0 - 127 = 18.104.22.168 (/1) = 128 /8 networks
CLASS B: 128 - 191 = 192.0.0.0 (/2) = 64 /8 networks or 16,384 /16 networks
CLASS C: 192 - 223 = 22.214.171.124 (/3) = 32 /8 networks or 2,097,152 /24 networks
CLASS D: 224 - 239 = 240.0.0.0 (/4) = 16 /8 networks or 268,435,456 multicast addresses
CLASS E: 240 - 255 = 248.0.0.0 (/5) = 8 /8 networks or ??? (I haven't a clue lol)
Hope that helps!!