The American Mathematical Society publishes detailed data about mathematics employment in the United States. In particular, the Report on New Doctoral Recipients has
"... information about the fall employment plans of doctoral recipients, a demographic profile summarizing characteristics of citizenship status, gender, and racial/ethnic group, the starting salaries, and other employment information about new doctoral recipients"
The data is always delayed by a year because of response and processing time. The most recent report as I write this is 2013-2014. My own take is as follows.
First, the statistics show that the overall unemployment rate is low: a new math PhD recipient is likely to be able to find a job of some sort immediately after graduation. In 2013-14, 85% of math PhD recipients were known to be employed immediately after graduation, and only 5% were known to still be looking (9% were unknown). This is partially due to the ability of mathematics PhDs to look for jobs in business, industry, and government, although the majority work in academia.
Second, based on my personal opinion and experience, the job market for postdocs and research-intensive tenure track positions is very competitive (this is true both in the U.S. and Europe, as well as some other countries and regions). You will need to be one of the very strongest candidates in your area to have a reasonable chance at such jobs.
Third, the market for tenure-track positions at non-research-intensive colleges is also competitive, but in a different way. For these, you want to have a strong vita showing teaching skill and research ability in line with the institution where you are applying. Simply having a PhD and teaching a handful of classes as an graduate student is unlikely to make you stand out from the other applicants.
Overall, because the job market is competitive, if you do enter a PhD program, you need to plan early for the career path you wish to follow. Simply "getting a PhD", and only worrying about the job market in your last semester, is not a good strategy. You want to begin shaping your vita early in your graduate program so that you are in a good position when you graduate.