Most digital cameras have the option of allowing you to record your images in the camera in both the RAW and JPEG file formats. That is to say, when you press the shutter you are simultaneously creating each of these files on your card. The main reason that this feature has been used for by me prior to coming to the Fuji system is when I wanted to give the images I was making to someone who wanted them there and then, and of course that meant that I needed a processed file that could allow me to do this. The raw file would still give me the insurance that I wanted (as raw files do).
Since the move to Fujifilm cameras (my own journey has been the x100 to the X-T1 and now the x100t and X-T1 as a killer combo for me) some of the limitations and strengths of these cameras have encouraged me to use the practice of shooting raw and jpeg full time. Memory cards are plenty big enough these days so there should be no obstacle to get the benefits below.
Check focus
I am told that the image that is rendered in the back of the camera's LCD when you are shooting in any format is actually a JPEG embedded as part of the RAW file for preview purposes, regardless of whether you are shooting RAW or the RAW/JPEG combination. However, this preview JPEG is too low a resolution to check your image at 100% for critical focus. However, when you shoot with the JPEG + RAW option enabled, with an L or better image size setting, you are able to zoom in to check at 100%, either on the back of the camera or on the EVF to check critical focus. Its a workaround for a quirky annoyance with Fujifilm firmware.
Film sims are good enough
I don’t need to relay it again as it has been echoed all over the internet that fujifilm JPEGs and the associated film simulations are beautiful. Often times I look at the jpegs rendered by the camera and there is absolutely nothing that I want to do except perhaps a crop, slight contrast boost and maybe a vignette if appropriate. You can save so much time in post processing looking at the jpegs first - if you are happy with them then save the time to go shooting! You still have the RAW file for any future processing you might want to do.
Print to instax or share
You cannot use the wifi feature on the newer Fujifilm cameras to transmit RAW files - you can only send a JPEG, so if you want to get some images off your camera and onto your phone or tablet, or to have some fun with the little instax printer, then you should be shooting the JPEG + RAW combo. Even though it is possible to render JPEGS from the playback menu it is so much more convenient to have this ready to go and combined with the other benefits offered from shooting JPEG - why not?