What characteristics of a ciphertext can be indicators of a particular cipher?

If I have a ciphertext, what information about the probable ciphers used can I infer from the ciphertext itself? For example, information from:

• the length


• the spacing / grouping of characters


• the range of characters used


• frequency counts

and any other information that is intrinsic to the ciphertext itself.

I'm talking about pencil-and-paper ciphers of the kind often used in cryptogram puzzles, rather than real, 'strong', modern forms of crypto.