Short answer: if you deal with IO, you deal with IOExceptions. If you don't deal with IO, then IOExceptions should be turned into unchecked exceptions, because they're symptoms of buggy code.
Longer answer:
readValue always takes a JsonParser, which may be wrapped around IO (e.g. a file or a URL). If you're dealing with IO, there's no way around dealing with IOExceptions, and you should either handle them or rethrow/pass them in some way. Anything can happen during IO, and you should be prepared to deal with the exceptions.
However, if you are sure that your JsonParser instances don't use IO (e.g. you used JsonFactory#createJsonParser(java.lang.String) to create a JSON parser on a string), you may assume that any IOExceptions you receive are bugs, either in your code or in Jackson. Usually, throwing an unchecked exception is then the proper way to deal with it:
ObjectMapper om = new ObjectMapper(/* whatever */);
JsonParser jp = JsonFactory.createJsonParser("{ \"foo\": \"bar\" }");
try {
return om.readValue(jp);
} catch (IOException e) {
throw new AssertionError("An IOException occurred when this was assumed to be impossible.");
}
Nota bene: my Java is rusty and I've never used Jackson, so consider the above block to be pseudocode.
In any case, you never need to declare AssertionError in throws, because they're unchecked exceptions. Everything that's a subclass of java.lang.RuntimeException or java.lang.Error doesn't need to be caught or rethrown explicitly. These exceptions are used for problems that are not expected to occur unless you're dealing with buggy code or when your VM's host is on fire.