MAME is in constant development. It currently has a cycle of approximately four weeks between updates (excluding major breakages). These updates can contain bug fixes, new machines and updated software lists. The problem is that these updates can seem to "break" systems that have worked before. However, this is not always the case, and a simple ROM file update can sort most of the problems. Please don't get confused with ROMs and software. A ROM file is an image of a chip from an original circuit board and software is loaded from media such as floppy disks, cd-roms or hard disks. To keep things simple, all the ROM files for a system are zipped into one file and are given the relevant machine name. Most arcade machines and computer systems will run with just these files, but some require software images as well.
When a new version of MAME is released, you will need to download the latest archive file and extract it over the old one. You can download the latest version of MAME from here. Just follow the mame Installation page and when it asks you to overwrite any files, answer "Yes". WARNING! If you have any edited or custom files, back them up before extracting the archive! Overwriting existing files shouldn't cause any problems with the general running of MAME however, updated machines may not work any more due to the required ROM files being changed.
If you have any issues with MAME after you have updated it, check out the Troubleshooting page where most issues are dealt with.