From MSDN:
This property returns null in the following cases:
1) if the specified key is not found;
So you can just:
NameValueCollection collection = ...
string value = collection[key];
if (value == null) // key doesn't exist
2) if the specified key is found and its associated value is null.
collection[key] calls base.Get() then base.FindEntry() which internally uses Hashtable with performance O(1).
Use this method:
private static bool ContainsKey(this NameValueCollection collection, string key)
{
    if (collection.Get(key) == null)
    {
        return collection.AllKeys.Contains(key);
    }
    return true;
}
    Yes, you can use Linq to check the AllKeys property:
using System.Linq;
...
collection.AllKeys.Contains(key);
However a Dictionary<string, string[]> would be far more suited to this purpose, perhaps created via an extension method:
public static void Dictionary<string, string[]> ToDictionary(this NameValueCollection collection) 
{
    return collection.Cast<string>().ToDictionary(key => key, key => collection.GetValues(key));
}
var dictionary = collection.ToDictionary();
if (dictionary.ContainsKey(key))
{
   ...
}
    I don't think any of these answers are quite right/optimal. NameValueCollection not only doesn't distinguish between null values and missing values, it's also case-insensitive with regards to it's keys. Thus, I think a full solution would be:
public static bool ContainsKey(this NameValueCollection @this, string key)
{
    return @this.Get(key) != null 
        // I'm using Keys instead of AllKeys because AllKeys, being a mutable array,
        // can get out-of-sync if mutated (it weirdly re-syncs when you modify the collection).
        // I'm also not 100% sure that OrdinalIgnoreCase is the right comparer to use here.
        // The MSDN docs only say that the "default" case-insensitive comparer is used
        // but it could be current culture or invariant culture
        || @this.Keys.Cast<string>().Contains(key, StringComparer.OrdinalIgnoreCase);
}
    
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