I won't address question of whether or not forecasting accurately is a viable goal or not, since for better or for worse, forecasting is here to stay, and progress in time series econometrics and dynamic modelling mean it's only growing in importance.
Moving beyond that debate, here are a few sources for economic forecasts that I've used in the past.
Free
- For general articles, the Wall Street Journal is a commonly-used source.
- You can often find economic forecasts by searching online for proceedings from various meetings; for example, here is a report from a meeting of the New York State Forecast Committee that describes forecasts for real GDP growth for 2013 and 2014.
- Forecasts.org has a page of forecasts for economic indicators is a nice source for quick forecast information. If you want more detailed forecasts from them, you'll need to subscribe, but they offer a great deal for free.
- The Congressional Budget Office publishes The Budget and Economic Outlook, which focuses on GDP, government deficits, etc.
- The Council of Economic Advisers publishes their Economic Report to the President on an annual basis; if you follow the links for each report, you'll see sections that discuss economic forecasts.
Subscription
Focus Economics is one of several companies that offers paid subscriptions to detailed economic forecasts. You can download samples (from July 2011) of their forecasts for the major economics, Euro area, Asia/Pacific, etc. The documents contain economic forecasts:

and general analysis:

The actual sample is 83 pages, so there is quite a bit of information there.
Consensus Economics is another company that provides paid subscriptions, albeit from different sources. They also publish tables of economic forecasts:

You can download samples of these forecasts for the world, the US, energy and metal markets, foreign exchange markets, Latin America, Eastern Europe, Asia/Pacific, as well as general current economic information, and others. The regional reports also provide foreign exchange forecasts for those regions, analysis, charts, etc.
Other
You can usually find sector-specific economic forecasts simply by searching online for organizations in that sector; for example, Fierce Biotech provides articles and general information about the biotech industry, and some of their analysis articles discuss forecasts for the sector. The National Association of Home Builders provides forecasts of the housing sector and related information. You could probably find similar information for other sectors.