Does Final Cut Pro X support all video files as did its prior version Final Cut Pro Studio?

Really depends on the specific file type you want to work with. FCP X does not support every single flavor of video FCP 7 did, so it's not a huge surprise if the file you're using is not supported. That said, there's plenty of free third party tools you could use to convert it to a regular QuickTime ProRes file that FCP X would accept. For example- http://www.squared5.com/ would most likely be able to load it. Try and let us know. And if that doesn't work please provide more details about the 3gps file you're using.

FCP7 and earlier did not support 3GP files. You could import them, but they did not work properly in an FCP sequence. As James said, FCPX may not support the the same formats, but it actually supports many more natively than did previous versions.

Try third party tool. I use this video converterwhich can help convert 3GP, mts, mxf files to apple prores MOV which FCP X can recognize. Many people said FCP can read almost all the video formats but under my experiences, it is not true. I have VRO and MXF files which are both beyond its ability.

3gp is not supported with FCP X, and you should first convert your 3gps to mp4, mov, or avi, then import the converted mp4, mov, or avi file o FCP X.

I am always using third party tool "Total Video Converter" from App store to convert my Youtube FLV files to iPhone, so great. And you will search it easily on App store.

But if your OS is lower than 10.6.6, you can search "Total Video Converter etinysoft" , and the first result is the same app as that on App store.