Just like your petrophysicist, your seismic processor has some awesome stuff that you want for your interpretation. She has velocities, fold maps, and loads of data. For some reason, processors almost never offer them up — you have to ask. Here is my processing product checklist:
A beautiful seismic volume to interpret. Of course you need a volume to tie to wells and pick horizons on. These days, you usually want a prestack time migration. Depth migration may or may not be something you want to pay for. But there's little point in stopping at poststack migration because if you ever want to do seismic analysis (like AVO for example), you're going to need a prestack time migration. The processor can smooth or enhance this volume if they want to (with your input, of course).
Unfiltered, attribute-friendly data. Processors like to smooth things with filters like fxy and fk. They can make your data look nicer, and easier to pick. But they mix traces and smooth potentially important information out—they are filters after all. So always ask for the unfiltered data, and use it for attributes, especially for computing semblance and any kind of frequency-based attribute. You can always smooth the output if you want.
Limited-angle stacks. You may or may not want the migrated gathers too—sometimes these are noisy, and they can be cumbersome for non-specialists to manipulate. But limited-angle stacks are just like the full stack, except with fewer traces. If you did prestack migration they won't be expensive, get them exported while you have the processor's attention and your wallet open. Which angle ranges you ask for depends on your data and your needs, but get at least three volumes, and be careful when you get past about 35˚ of offset.
Rich, informative headers. Ask to see the SEG-Y file header before the final files are generated. Ensure it contains all the information you need: acquisition basics, processing flow and parameters, replacement velocity, time datum, geometry details, and geographic coordinates and datums of the dataset. You will not regret this and the data loader will thank you.
Processing report. Often, they don't write this until they are finished, which is a shame. You might consider asking them to write up a shared Google Docs or a private wiki as they go. That way, you can ensure you stay engaged and informed, and can even help with the documentation. Make sure it includes all the acquisition parameters as well as all the processing decisions. Those who come after you need this information!
Parameter volumes. If you used any adaptive or spatially varying parameters, like anisotropy coefficients for example, make sure you have maps or volumes of these. Don't forget time-varying filters. Even if it was a simple function, get it exported as a volume. You can visualize it with the stacked data as part of your QC. Other parameters to ask for are offset and azimuth diversity.
Migration velocity field (get to know velocities). Ask for a SEG-Y volume, because then you can visualize it right away. It's a good idea to get the actual velocity functions as well, since they are just small text files. You may or may not use these for anything, but they can be helpful as part of an integrated velocity modeling effort, and for flagging potential overpressure. Use with care—these velocities are processing velocities, not earth measurements.
Surface elevation map. If you're on land, or the sea floor, this comes from the survey and should be very reliable. It's a nice thing to add to fancy 3D displays of your data. Ask for it in depth and in time. The elevations are often tucked away in the SEG-Y headers too—you may already have them.
Fold data. Ask for fold or trace density maps at important depths, or just get a cube of all the fold data. While not as illuminating as illumination maps, fold is nevertheless a useful thing to know and can help you make some nice displays. You should use this as part of your uncertainty analysis, especially if you are sending difficult interpretations on to geomodelers, for example.
I bet I have missed something... is there anything you always ask for, or forget and then have to extract or generate yourself? What's on your checklist?