ASN1_BCD_STRING (64): Represents a string with the following characters: "0123456789*#+-. " (excluding the quotation marks). Each octet encodes two characters, where the high nybble corresponds to the first character and the low nybble corresponds to the second character.
ASN1_PC_STRING (65): Represents a string of characters in the PC character set. Note that the control characters can also be used as graphic characters.
ASN1_TRON_STRING (66): Represents a string of characters in the TRON character set, encoded as TRON-8.
ASN1_KEY_VALUE_LIST (67): Represents a set of keys (with no duplicate keys) and with a value associated with each key. The encoding is the same as for a SET of the keys, but with the corresponding value immediately after each key (when they are sorted, only the keys are sorted and the values are kept with the corresponding keys).
ASN1_UTC_TIMESTAMP (68): Represents a number of UTC seconds (and optionally fractions of seconds), excluding leap seconds, relative to epoch.
ASN1_SI_TIMESTAMP (69): Represents a number of SI seconds (and optionally fractions of seconds), including leap seconds, relative to epoch.
ASN1_UTC_TIME_INTERVAL (70): Represents a time interval as a number of UTC seconds. The number of seconds does not include leap seconds.
ASN1_SI_TIME_INTERVAL (71): Represents a time interval as a number of SI seconds (which may include fractions).
ASN1_OUT_OF_BAND (72): This type is not for use for general-purpose data. It represents something which is transmitted out of band (e.g. a file descriptor) with whatever transport mechanism is being used. The transport mechanism defines how a value of this type is supposed to be encoded with whatever ASN.1 encoding is being used.
ASN1_MORSE_STRING (73): Represents a string of characters in the Morse character set. The encoding is like a relative object identifier, where 0 means an empty space, and others is like bijective base 2 with 1 for dots and 2 for dashes, with the high bit for the first dot/dash, e.g. 4 means A and 8 means U.
ASN1_REFERENCE (74): A reference to another node within the same file. (Not all implementations will support this feature.) The encoding is like a Relative Object Identifier; the first number is how many times to go to the parent node (where 0 means the reference itself), and then the rest of the numbers specify which child node of the current node to go to where 0 means the first child, 1 means the second child, etc. It can reference a primitive or constructed node of a BER file, but you cannot specify a child index for a child of a primitive node, since primitive nodes cannot have child nodes. At least one number (how many levels of parents) is required, but any number of numbers is potentially possible.
ASN1_IDENTIFIED_DATA (75): Data which has a format and/or meaning which is identified within the data. The encoding is always constructed and consists of two or three items. The first item is a set of object identifiers, object descriptors (used only for display), and/or sequences where the first item of the sequence is a object identifier. The receiver ignores any items in this set that it does not understand. The second item in a ASN1_IDENTIFIED_DATA can be any single item of any type; it is interpreted according to the object identifiers in the first set that the receiver understands. The third item is optional, and if it is present it is a key/value list of extensions; the keys are object identifiers and the values are of any type according to the object identifiers. The default value of this key/value list is an empty key/value list.
ASN1_RATIONAL (76): Stored as constructed, containing two integers, being the numerator and the denominator. The denominator must be greater than zero. If it is canonical form, then it must be lowest terms.
ASN1_TRANSLATION_LIST (77): A key/value list where the keys identify languages. If the key is null then it means the default in case no language present in this list is applicable. The types of the values depends on the application (usually they will be some kind of character strings).
In addition, the same number for the BMP string type can also be used for a UTF-16 string type, and there is a "OBJECT IDENTIFIER RELATIVE TO" type which encodes a OID as either relative or absolute (in canonical form, it is always relative when possible) in order to save space; the schema will specify what it is relative to. ANY and ANY DEFINED BY are allowed despite being removed from the most recent versions of standard ASN.1. (The schema format for these extensions is not defined, since I am not using the ASN.1 schema format; however, someone who does use it might do so if they need it.)
There is also SDER, which is a superset of DER but a subset of BER, in case you do not want the mess of BER but do not want to require strictly canonical form either; and also SDSER which uses the same encoding for types and values than SDER but but length works differently in order to support streaming better.
As is usual, you do not have to use any or all of these types, but someone might find them useful for some uses. I have used some of them in my own stuff.