The short answer is "yes" -- you have quite a large number of options for free video editing software, actually. There are commercial options, as well, but these often cost (at least) hundreds of dollars, and unless you have professional aspirations, you can probably find all the functionality you need with a free software option (also called "freeware").
As you start exploring your freeware video editing options, you do want to keep in mind a few issues. First, freeware doesn't come with the same level of customer support you'd expect for software you've actually purchased. However, you can usually see how often the author or developer of the freeware updates the product and what kind of support materials are provided upfront. You can also find lots of user reviews of various freeware, not just from the casual user, but from real tech geeks as well. There are a number of sites where you can find the freeware (such as www.freeware-guide.com and www.topfreeware.net, but search for "freeware" and "video editing," and you'll find even more). You'll find reviews and user statistics there, as well. Also make sure that the freeware provides you with a General Public License (GNU), so you know you can use it for free.
When considering which specific freeware video editing program is best for you, you need to think about what sort of files the program can handle, and what platforms and operating systems it works on. Microsoft and Apple each have pretty good freeware video editing programs, but they run on their operating systems only (Apple's version is only free when bought with a new Apple system). Your computer will also need enough processing power to handle the video editing software, so check the spec requirements before you download. You also want to check out how many visual effects features the program provides; although keep in mind that add-ons may be available that increase that program's overall effects library.