In my opinion RSACryptoServiceProvider class is seriously under-documented in MSDN. Since there is also no abundance of examples on the web, I spent more time than I should figuring out how to use it correctly. For future reference I'm listing below the solution to two problems I had.

The maximum byte array length for encrypting without OAEP padding is Modulus size - 11 which is written somewhere in the Encrypt() method documentation. If you pass it a larger array it will return a not so informative Unspecified error. To encrypt a larger chunk of data you have to split it in smaller parts, encrypt them individually and concatenate them back together. You have to do the same when decrypting the data, with the only difference that each part has the size of Modulus in stead of Modulus - 11. To get the modulus size you can use the following piece of code (rsa is an instance of RSACryptoServiceProvider):

RSAParameters rsaParams = rsa.ExportParameters(false);
int modulusSize = rsaParams.Modulus.Length;

Each time you instantiate RSACryptoServiceProvider it generates a new pair of keys. If you want to use existing ones, you can import them by calling:

rsa.FromXmlString(key);

The key parameter is a string with the XML representation of the keys. You can get it by calling the ToXmlString() method once and storing its results. It's only parameter specifies whether to also export the private key. I guess I don't have to remind you that you need the private key only for decryption and that you should always keep it private for the encryption to make any sense at all.