Depending on how much you know about the input, you may have to take into account that not all Unicode characters are valid XML characters.

Both Server.HtmlEncode and System.Security.SecurityElement.Escape seem to ignore illegal XML characters, while System.XML.XmlWriter.WriteString throws an ArgumentException when it encounters illegal characters (unless you disable that check in which case it ignores them). An overview of library functions is available here.

Edit 2011/8/14: seeing that at least a few people have consulted this answer in the last couple years, I decided to completely rewrite the original code, which had numerous issues, including horribly mishandling UTF-16.

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;

/// <summary>
/// Encodes data so that it can be safely embedded as text in XML documents.
/// </summary>
public class XmlTextEncoder : TextReader {
    public static string Encode(string s) {
        using (var stream = new StringReader(s))
        using (var encoder = new XmlTextEncoder(stream)) {
            return encoder.ReadToEnd();
        }
    }

    /// <param name="source">The data to be encoded in UTF-16 format.</param>
    /// <param name="filterIllegalChars">It is illegal to encode certain
    /// characters in XML. If true, silently omit these characters from the
    /// output; if false, throw an error when encountered.</param>
    public XmlTextEncoder(TextReader source, bool filterIllegalChars=true) {
        _source = source;
        _filterIllegalChars = filterIllegalChars;
    }

    readonly Queue<char> _buf = new Queue<char>();
    readonly bool _filterIllegalChars;
    readonly TextReader _source;

    public override int Peek() {
        PopulateBuffer();
        if (_buf.Count == 0) return -1;
        return _buf.Peek();
    }

    public override int Read() {
        PopulateBuffer();
        if (_buf.Count == 0) return -1;
        return _buf.Dequeue();
    }

    void PopulateBuffer() {
        const int endSentinel = -1;
        while (_buf.Count == 0 && _source.Peek() != endSentinel) {
            // Strings in .NET are assumed to be UTF-16 encoded [1].
            var c = (char) _source.Read();
            if (Entities.ContainsKey(c)) {
                // Encode all entities defined in the XML spec [2].
                foreach (var i in Entities[c]) _buf.Enqueue(i);
            } else if (!(0x0 <= c && c <= 0x8) &&
                       !new[] { 0xB, 0xC }.Contains(c) &&
                       !(0xE <= c && c <= 0x1F) &&
                       !(0x7F <= c && c <= 0x84) &&
                       !(0x86 <= c && c <= 0x9F) &&
                       !(0xD800 <= c && c <= 0xDFFF) &&
                       !new[] { 0xFFFE, 0xFFFF }.Contains(c)) {
                // Allow if the Unicode codepoint is legal in XML [3].
                _buf.Enqueue(c);
            } else if (char.IsHighSurrogate(c) &&
                       _source.Peek() != endSentinel &&
                       char.IsLowSurrogate((char) _source.Peek())) {
                // Allow well-formed surrogate pairs [1].
                _buf.Enqueue(c);
                _buf.Enqueue((char) _source.Read());
            } else if (!_filterIllegalChars) {
                // Note that we cannot encode illegal characters as entity
                // references due to the "Legal Character" constraint of
                // XML [4]. Nor are they allowed in CDATA sections [5].
                throw new ArgumentException(
                    String.Format("Illegal character: '{0:X}'", (int) c));
            }
        }
    }

    static readonly Dictionary<char,string> Entities =
        new Dictionary<char,string> {
            { '"', "&quot;" }, { '&', "&amp;"}, { '\'', "&apos;" },
            { '<', "&lt;" }, { '>', "&gt;" },
        };

    // References:
    // [1] http://en.wikipedia.org/wiki/UTF-16/UCS-2
    // [2] http://www.w3.org/TR/xml11/#sec-predefined-ent
    // [3] http://www.w3.org/TR/xml11/#charsets
    // [4] http://www.w3.org/TR/xml11/#sec-references
    // [5] http://www.w3.org/TR/xml11/#sec-cdata-sect
}

Unit tests and full code can be found here.