Will there be data loss if I upgrade?

According to the documentation:

Renewing the Installation without formating the partitons (in contrast to upgrading), will also keep the personal data and configurations under /home but will renew all system settings under /etc as well as the default set of installed packages.

However, it is impossible to upgrade from 8.10 directly to 10.04. You would need to upgrade to 9.04, then 9.10, and then finally 10.04. This can be a long and painstaking process, so in your case I would recommend doing a new install over your existing install, which will not format your drive. (More detail here). The installer will preserve the data in your home directory but do an install over the rest of the system.

As always with every upgrade please make sure you backup your important data.

You can upgrade all currently supported versions of Ubuntu (Ubuntu 12.04/14.04/16.04) without losing your installed applications and stored files. Packages should only be removed by the upgrade if they were originally installed as dependencies of other packages, or if they conflict with newly installed packages. Upgrades between Long Term Support (LTS) releases are not enabled by default until the first point release. It is recommended that most LTS users wait until then before upgrading.

You can also upgrade Ubuntu without deleting Windows or losing your Windows files if you are dual booting Ubuntu with Windows.

Backing up all your personal files before upgrading is still advised in case anything goes wrong with the upgrade. Once I installed Ubuntu in VirtualBox and immediately upgraded it to the next version, but I still got some error messages while upgrading. This illustrates how prone to errors upgrading can be, which is why you should backup your data before upgrading. Despite those error messages, Ubuntu worked perfectly after upgrading it.

I up-voted Jorge's answer. However, I always back up all documents onto another hard drive and perform a 100% new install. Everything seems to work better that way. I also use "save markings" in Synaptic to reinstall all my packages. In ANY scenario, I have no trust my data will be preserved! There is too much at stake.

For what it's worth, I have done the upgrade route. It took a long time, but I didn't lose any data in the process. The trickiest thing is that you do have to tackle any hardware incompatibilities that might have plagued each release. With 9.10 in particular I had major video problems that would black out my screen--making solving the problem pretty tricky! So in theory upgrading through several releases does work without data loss, but in practice it can be a real hassle.

You can do a fresh install, though, without backing up to a separate hard drive (or losing your data) if you set up a separate partition on your hard drive for your /home folder. Then just do a fresh install of the operating system and choose the main partition for the OS installation during the setup process. Either during setup or afterward (using GParted) you can mount the partition with all of your user data to the /user location again and you're ready to go. If you Google it, there are quite a few good articles that walk you through the process.

Of course, the actual software still needs to be installed again, even with a separate /home partition. But the trade-off is that your OS partition can be set up using a newer file system like ext4 that will give you better performance. If you do have to reinstall your applications, the new Software Center makes it pretty easy and quick. Also, I'd recommend installing Ubuntu Tweak early in the process, since it gives you a nice quick interface for setting up common outside repositories (like medibuntu or the Mozilla repos) that would otherwise involve some surfing around to find the PPA addresses.