Absolutely, personally I dislike how it's the single most powerful figure for decisionmakers. There have been many alternative measurements developed for measuring overall progress of an economy, but unfortunately they haven't taken much foothold.
The problem is not so much GDP, as it is to measure the economy in one float. So GDP is a somewhat good measure, if you want a quick handle on production capacity, for standard of living something like purchase parity median income is better, but tells you nothing about relative strength of exports, etc...
If we stick to "economics" without even going to "well-being," I think median net worth is the best bet. But you know, governments find it easier to "book" corporate profits as part of GDP and call it a day.
On the more economic side, you have something like the Misery Index and its extensions (http://www.cato.org/publications/commentary/misery-mena). Obviously composite indexes like these have their flaws too, but overall they are more comprehensive than GDP alone.