How can I find already-reduced Spitzer data?
Spitzer started a completely new kind of observing program, called Legacy programs. These are large, coherent data sets (organized around a scientific theme), and the observers agreed to waive their proprietary rights, e.g., they let their Spitzer data go public immediately. If that weren't enough, they also deliver back to the SSC so-called enhanced data products, which are, at minimum, reduced Spitzer data, but often include observations at other wavelengths as well.
You can read all about the Spitzer Legacy program on the SSC website, and if you go to the list of all Legacy programs, you can see what a tremendous variety of programs there are. Each program has a plan of what they will deliver back to the SSC and when - that can be obtained by clicking on the blue dot on the far right of that page, one per Legacy program. The oldest Legacy programs have had the longest time to work on their data, so they are the ones that have delivered the most data back to the SSC. The newest programs in many cases haven't even obtained their data yet.
Why would you want to use data from these projects? (a) They have used observing strategies that in many cases broke their observations over several AORs, and they have already done the work of combining multiple AORs where necessary. They have used their expertise to create the best possible mosaic from these data; (b) They have (in many cases) already done the photometry for you as well, so you can just jump in and get the fluxes directly from them right away; (c) I guarantee you that the original astronomers who designed these observations and created these mosaics and photometry have NOT had time (and probably never will have time) to extract every little bit of information out of them. There is a LOT of science just waiting to be discovered in these data!
Which objects are in these projects? These projects do not cover the whole sky. They're not even everything that Spitzer has ever observed. But they are a lot of data anyway. If the object in which you are interested is lucky enough to be in one of these regions, then by all means, take advantage of it! There is no one master list of all of the things that are just in Legacy projects. You kind of have to poke around on your own to see if your object is in one of these regions. If you use Leopard to search for prior observations, and one of the programs that is returned by your search is a Legacy program, e.g., is listed on the complete list of Legacy projects, then probably you will be able to get data products from the Legacy teams for your object. Remember, though, it takes time for the teams to chew through the data, so it's possible that the data have been taken but not yet returned as enhanced products to the SSC.
Example: getting images of M51 from the SINGS program
The SINGS program observed a long list of nearby galaxies with IRAC and MIPS. If you go to the list of Legacy projects, you can find the SINGS team website, an overview paper about SINGS, and a list of their data deliveries. This is one of the oldest projects, so they have had five deliveries, including their final delivery. They deliver images (in Spitzer and optical wavelengths) and Spitzer spectra. As I type this, their final delivery has not yet been fully ingested into IRSA, which will be its permanent home after the Spitzer Science Center shuts its doors for good. But you can either access the most recent version of the data directly by clicking on "direct data access," or use IRSA to search their second-to-last delivery (probably good enough for most purposes).
If you'd like images of M51, the Whirlpool galaxy, go to "direct data access" and find the directory for NGC 5194 (which is a synonym for M51). In that directory, you'll find a directory for IRAC, MIPS, IRS, and "Ancillary". Each of these directories contains fits images (final mosaics) of this object in those wavelengths. The "Ancillary" directory includes BVRI and Halpha images.
These data are all free for your use.
Example: getting images and photomety of M16 from the GLIMPSE program
The GLIMPSE program is actually three generations of programs that surveyed/is surveying a large portion of the galactic plane with IRAC. (NB: it has a sister program, MIPSGAL, which is doing the same region with MIPS.) If you go to the list of Legacy projects, you can find the GLIMPSE team website, an overview paper about GLIMPSE, and a list of their data deliveries, where it becomes apparent that there are three generations of this program all listed together on one page. The original GLIMPSE program is one of the oldest projects, so they have had many deliveries. They deliver images and catalogs. They have delivered so much data that, unlike SINGS above, this time you really do want to search via IRSA because otherwise it's too hard to find what you want.
M16, the Eagle Nebula, is in the region covered by GLIMPSE. If you'd like images of M16, click on "IRSA search" and search on M16. The search will return several "postage stamp" image cutouts of the region, at different resolutions. Go down to the bottom of the returned page to download them.
If you'd like source lists (extracted photometry) from M16, you need to use Gator to the GLIMPSE catalog -- this works just like searching the 2MASS catalog using Gator if you've done that before. Type "M16" in as the object name, and whatever search radius you would like, and it will come back with a list of objects in that region and fluxes at all four IRAC bands, along with a bunch of other information (like quality flags), just like 2MASS.
These data are all free for your use.