Obviously not many people will actually have trophy cabinets (I don't), and plenty of us won't actually have anything which is 'strictly' (ask James Robinson

Mine would include:
A bronze medal from the UK Maths Trust Junior Maths challenge, back when I was young enough.
A silver medal from when my school did a fantasy football competition. This season is in fact the first time I've played fantasy football since then, and it's reminded me why - it's a huge timesink for me.
A trophy from when I won the only chess tournament my secondary school ever held - this was the same tournament where a teacher told me off for checkmating someone in four moves (yes, really).
A glass lump for doing well in my MSc exams. It's called the 'Pfizer award for excellence in statistics' (or something like that), and is awarded to whoever performs best in that year's MSc Stats exams at UCL. I was pretty amused when I found out I'd won it, and I ended up having to go Sandwich to walk around the Pfizer building there for a bit, which was pretty boring. I did get to eat a sandwich in Sandwich, though, which means I am a badass.
The Co:Lon 2010 trophy. 'nuff sed.
Edit: Totally forgot the trophies we got from Pointless, lulz.