Avoid collisions, replace the hub with a switch.
Advantages of a home server? Well, my small home server does quite a lot really.
It acts as an 'internet gateway' / DIY "router" (aka good old NAT). It's a really rather flexible firewall. I have traffic shaping, though I haven't made too much use of it. These actually sort of go hand in hand - all handled with pf. I actually love this setup, and have done my best to avoid a normal boring commercial home router £50 thing

It's a Windows domain server, and allows users to log on to it and have roaming profiles. It is a [very] small file server, so important user data can be saved to it's RAID-1 arrays. What does this mean? It means if I have to format, when I have re-joined the domain and go to log on afterwards, it's much the same! My firefox favourites remain, all my e-mails are still there (without backing up. at all) etc. Most Windows options are saved in the roaming profile, and for those that aren't I've got a log on script and policy which do a lot of it automatically anyway. Basically, I don't have to do any reconfiguring of Windows to get it how I like it after a format! It's fab.
It's a small web-server. I've designed a small simple dynamic 'intranet' for the family, which can save links, has search boxes for google, images and ebay with search history. It has a small file upload facility, which actually uploads to the site on the same machine which is accessible via the internet (the public facing site). This is per user, so it's semi-personalised. It just makes things a tiny bit easier.
I run a small caching name server. This allows me to do Windows 'hosts file' style domain blocking on a global network basis.
I run a time server. It continuously syncs it's time with multiple other time servers around the world, and my Windows machines sync to it both in the log on script, and then automatically every hour to keep clocks in sync.
I used to have a static IP (8 actually), but no longer. I can still run a dynamic DNS client, which then allows me to use SSH to remotely admin the machine, if needs be.
I do have an FTP server running accessible internally only, but that hasn't actually been used for a good while. It can be handy sometimes, and sometimes I will quickly let it pass the firewall for various tasks. Rare though.
I might even run a self coded MSN sniffer / logger, which can log any MSN messages passing through that machine (login to MSN inside my network, I get to invade yer privacy

)

I could log other things, like any sites visited for a particular machine etc.
I used to run and make use of a local IMAP / mail server. I used a script to grab new e-mail from my hotmail account and dumped them to a local server, which I could then connect to with a proper e-mail client. Thunderbird now has a plugin to get hotmail messages, so it's a bit redundant.
Most importantly, it creates my sig image with some stats about its self, and uploads it to a now rather dodgy free FTP hosting lala every hour

That's not using a Windows machine before you ask "how do I do...", but there should still be a fair few things you can do with some kind of central small server.