I have the same issue as xpragmaticx. My 00 Accord EX (4 cylinder, 141K miles) burns about 1 quart every 1000 miles. The Honda dealer told me that this is normal on high mileage Accords.
I just top it off every 2nd or 3rd oil change.
Question: if it burns 1 quart every 1000 miles, then it'll burn 3 quarts when it's due for an oil change at 3K miles. My Accord only takes around 5 quarts of oil anyway, so I'll only have 2 quarts left at my oil change. Is that normal?