Speaking of all the security issues in general, but leaving out the viruses, Ubuntu has build-in security.
However, Ubuntu will not stop you from installing malware like the Windows anti-viruses try to do. For example, if someone tricks you into installing software that will spy, spam, or destroy all your data then you're out of luck.
Many more security mechanisms are available if you choose to set them up: firewall rules, anti-virus scanners, network monitoring, two-factor authentication, etc... These additional mechanisms are mostly intended for servers and you should not need to worry about them as a desktop user.
Having that said, there are many vulnerabilities and Linux systems get broken into every day all over the world. Security teams come-out with updates to fix these vulnerabilities regularly. Ubuntu has it's own security team that releases updates and advices for systems administrators.
Here is an overview about anti-Viruses and Ubuntu security.
In practice Ubuntu is much safer than Windows. In terms of exposure to malware, Ubuntu is comparable to Mac. But as @Giacomo pointed out, living in a nearly virus free world can leave Mac users naive.
The top 2 things that you can do to stay extra safe:
- Install software only from the official repository
- Keep your software up by letting the Update Manager do it's thing