Your image will ultimately be displayed at depth of 8-bits per channel (technically, it's actually a 24-bit image, with three 8-bit channels, as opposed to an actual 8-bit image, such as you'd have with a Gif). There are some specific advantages to working in higher bit-depths, but if you're not exploiting those advantages, then it's likely that all you are doing is wasting disk space and cutting yourself off from some tools. I'll do my best to describe the advantages so you can decide if it's worth it.

If you're working with height maps (aka Digital Elevation Maps (DEMs) or displacement maps), then a higher bit depth allows more detail and reduces the problem of "terracing." With 8-bit color, you have only 256 discrete altitudes, and that can cause some serious problems, particularly if your height map is not normalized to use the entire range of 0 - 255. Working with a 16- or 32-bit height field means that you'll have more gradual changes in elevation.

If you need physically accurate lighting behavior, then 32-bit depth allows you to work with a linear gamma response. An explanation of gamma would take a bit longer than I want to spend here, but suffice to say that your computer monitor cannot display all luminance levels equally well. So some of the values in the images you see are boosted to compensate. This is true of most digital images. However, in the real world light doesn't behave that way. Linear light processing is typically only needed by scientists, architectural visualizers, and visual effects artists (and maybe a few other fields that I am not aware of).

High Dynamic Range imaging (HDRi) requires higher bit-depths in order to store the wide range of detail present from the darkest to the brightest areas in an image. Again, though, even an HDRi will ultimately be viewed in an 8-bit medium unless you're doing some serious gallery quality prints. The high bit depth image is reserved for source material and intermediate processing.

If you find a need to work in a high bit depth, but you need access to 8-bit filters, you have to work in two documents, copying and pasting between them. Just remember that every time you paste a layer from a high depth to a lower depth document, you will lose data, so try to only do it once per layer, and when you bring it back, don't trash the original layer, just in case you need that data back.