It really depends on the cigar. Some get chucked after an inch or so if they suck. Most of mine get thrown out with an inch or 2 left when they start to get bitter and acrid. Some are great all the way to the nub, and I throw them out when I can no longer smoke it without burning my lips.

Don't feel bad about tossing a cigar early. No point in suffering through it. Although on the flip side some cigars will start out weak, and develop into something real nice.