This isn't to say that they won't ever be a threat for a desktop Linux user, rather that it's highly unlikely. Nevertheless, there are some basic security practices that should be made part of your routine.
Run Security Updates – Whether for Ubuntu or something else altogether, keep those security updates current.
Secure Ports – If you don't need a port open, close it. A great GUI firewall manager is Gufw.
SSH RSA keys – For the sake of sanity, don't use weak passwords when running SSH on your Ubuntu box. Over the course of a day, you'll find countless attacks on your SSH port trying to crack what might be a weak password setup. I recommend using RSA keys instead. This prevents an attacker from "cracking" into your SSH setup via a password exploit.
Minimize attacks – Even though simply using RSA keys will help better secure your SSH setup, adding DenyHosts to the mix is good advice. This will keep malicious users from hitting your system and eating up resources, plus it will keep your log file a lot smaller.
There are countless additional things that can be done to further secure an Ubuntu installation, but these are the big things to consider. Now you may have noticed that I didn’t mention encryption of your home directory. For newbies, I'm against the idea of encrypting your home directory, simply because most people screw something up and lose their data.
For those set on encryption, however, my advice is to make a backup of your data BEFORE attempting to encrypt your home directory. Once you've done this, you can follow this guide to get you started in better securing your local home directory data.
Everything above will provide you with a solid primer for better securing your data and keeping yourself free from exploits. But there is one last consideration that is, perhaps, the biggest untapped threat yet.
Anything executable is dangerous
I realize it must sound paranoid to say that anything that can be executable on an Ubuntu installation is a potential risk. Yet when you stop to think about it, for new users, it absolutely is a massive risk being completely ignored.
From mystery Deb packages to unknown PPA repositories, unless these things have been vetted by a trusted source you’re playing with fire.
Thus far we've been fortunate and no one has released a dangerous package to the Ubuntu-using masses. And if users simply stick to trusted software sources only, they will never experience a problem in this area.
But when you consider the vast amount of bash/python scripts and other little Ubuntu tweak-related hacks, it's clear that users need to pay close attention to what these changes are doing to their system. All one has to do is blindly grant root privileges to run a dangerous script or install malicious software, and the typical end user would be in real trouble.
Again, thus far nothing has gone horribly wrong...but this doesn't mean that this approach should continue to be encouraged. Instead, I strongly advise new users to only grab software from trusted sources. We know that trusted sources like the official Ubuntu repositories are safe to use. Though it might seem paranoid, for newbies I recommend sticking with this source exclusively for software.
Think I'm overstating how dangerous random scripts can be? Take a look at this list of very basic examples. All it takes is blindly allowing root privileges and it's game over.
The biggest security threat out there
The biggest security threat to an Ubuntu installation isn't what we'd normally consider to be malware. No, the single most dangerous thing that can happen to your data is executing random code without fully grasping what it does.
Even something as benign as configuring hdparm incorrectly can go beyond what most malware can do – it can flat out ruin your hard drive if used improperly, though not visibly with immediate damage.
So, with the understanding of how important it is to be careful, the best security suite available for Ubuntu users will never be purchased from a store shelf. The best security is knowledge and the willingness to spend a little time reading up on how to properly secure your Ubuntu system.
By following the basic tips found under the "good offense" section above, odds are you won't ever have any security problems.