Multi-threaded application interaction with logger thread

It seems it should be working. Producers-Consumers shouldn't change greatly in case of single consumer. Little nitpicks:

• acquiring lock may be an expensive operation (as @Vitaliy Lipchinsky says). I'd recommend to benchmark your logger against naive 'write-through' logger and logger using interlocked operations. Another alternative would be exchanging existing queue with empty one in GetLog and leaving critical section immediately. This way none of producers won't be blocked by long operations in consumers.

• make LogObj reference type (class). There's no point in making it struct since you are boxing it anyway. or else make _queue field to be of type LogObj[] (that's better anyway).

• make your thread background so that it won't prevent closing your program if Stop won't be called.

• Flush your TextWriter. Or else you are risking to lose even those records that managed to fit queue (10 items is a bit small IMHO)

• Implement IDisposable and/or finalizer. Your logger owns thread and text writer and those should be freed (and flushed - see above).

While it appears to be thread-safe, I don't believe it is particularly optimal. I would suggest a solution along these lines

NOTE: just read the other responses. What follows is a fairly optimal, optimistic locking solution based on your own. Major differences is locking on an internal class, minimizing 'critical sections', and providing graceful thread termination. If you want to avoid locking altogether, then you can try some of that volatile "non-locking" linked list stuff as @Vitaliy Lipchinsky suggests.

using System.Collections.Generic;
using System.Linq;
using System.Threading;

...

public class Logger
{
    // BEST PRACTICE: private synchronization object. 
    // lock on _syncRoot - you should have one for each critical
    // section - to avoid locking on public 'this' instance
    private readonly object _syncRoot = new object ();

    // synchronization device for stopping our log thread.
    // initialized to unsignaled state - when set to signaled
    // we stop!
    private readonly AutoResetEvent _isStopping = 
        new AutoResetEvent (false);

    // use a Queue<>, cleaner and less error prone than
    // manipulating an array. btw, check your indexing
    // on your array queue, while starvation will not
    // occur in your full pass, ordering is not preserved
    private readonly Queue<LogObj> _queue = new Queue<LogObj>();

    ...

    public void Log (string message)
    {
        // you want to lock ONLY when absolutely necessary
        // which in this case is accessing the ONE resource
        // of _queue.
        lock (_syncRoot)
        {
            _queue.Enqueue (new LogObj (DateTime.Now, message));
        }
    }

    public void GetLog ()
    {
        // while not stopping
        // 
        // NOTE: _loggerThread is polling. to increase poll
        // interval, increase wait period. for a more event
        // driven approach, consider using another
        // AutoResetEvent at end of loop, and signal it
        // from Log() method above
        for (; !_isStopping.WaitOne(1); )
        {
            List<LogObj> logs = null;
            // again lock ONLY when you need to. because our log
            // operations may be time-intensive, we do not want
            // to block pessimistically. what we really want is 
            // to dequeue all available messages and release the
            // shared resource.
            lock (_syncRoot)
            {
                // copy messages for local scope processing!
                // 
                // NOTE: .Net3.5 extension method. if not available
                // logs = new List<LogObj> (_queue);
                logs = _queue.ToList ();
                // clear the queue for new messages
                _queue.Clear ();
                // release!
            }
            foreach (LogObj log in logs)
            {
                // do your thang
                ...
            }
        }
    }
}
...
public void Stop ()
{
    // graceful thread termination. give threads a chance!
    _isStopping.Set ();
    _loggerThread.Join (100);
    if (_loggerThread.IsAlive)
    {
        _loggerThread.Abort ();
    }
    _loggerThread = null;
}