I really like this game because it's basically just FOSS Mario Kart. It has a lot of gamemodes, an (admittedly simple) kart stat system, many tracks and a lot of mods.
OpenTTD
In OpenTTD, you transport cargo and people to different places. You can transport them using trains, buses, aeroplanes (airplanes if your American), boats and trams if you add a NewGRF (a mod). It is very addictive and it is quite easy to get into (except the signals).
Pingus
It's FOSS Lemmings with penguins.
Extreme Tux Racer
You play as Tux (or someone else) and slide yourself through terrain while you collect fish. It is fun, however I've found that it can get a bit repetitive. You can design levels, however it's a bit hard to do.
But back in 1997, I had the shareware version of Transport Tycoon and I’d come home from school (6th grade) in summer, about 20 minutes walk in 30 degrees heat - my dad would have the dodgy air conditioner on, I’d splash some water on my face and get down to some railroads.
It was a very good time and as an adult I’ve never recaptured that feeling with OpenTTD. But I still install it first thing in every distro.