Actually, according to the Buddhist monastic code they aren't allowed to have money. I know a very large number (probably the majority) of monks these days do accept money but I know of and have lived with those that don't. In the communities that respect the Vinaya[1] there are 227 rules that fully ordained monks are supposed to follow. Novices have ten rules[2] and one of them is not to handle money.

[1]http://www.accesstoinsight.org/lib/authors/thanissaro/bmc1/b...

[2]http://www.accesstoinsight.org/ptf/dhamma/sila/dasasila.html