I just checked the current version of the Microsoft C♯ Language Specification Version 4.0, and there is no mention of a limit in §1.6.4, §1.9, §10.1.4, §10.1.4.2 and §13. There is also no syntactic limit in the grammar in §B.2.7.
I obviously didn't read the entire 500 pages, but I don't know where else in that document a limit might be mentioned.
Note: this only applies to Microsoft C♯, and only to Version 4.0. I didn't check earlier versions of Microsoft C♯, nor did I check ECMA/ISO C♯. Also, it only applies to C♯, there might be limits in the CLI.
And last but not least, there might be implementation-specific limits in both Microsoft Visual C♯ and Novell Mono C♯, as well implementation-specific limits in Microsoft's and Mono's implementations of the CLI (i.e. the CLR and the Mono VM).
However, the question was about C♯, not about any particular implementation of C♯ and not about the CLI, so I feel pretty confident in claiming that the number of interfaces a class can implement is unbounded.