This are some software ideas I've had that I'd like to try sometime. If you want to do them, go ahead. Feel free to email me.
Use wiktionary, wikipedia and genetic algorithms to make a parse tree for english
Idea
A parse or syntax tree for a the english language, much like a syntax tree for programming languages. English is defined by usage. How about getting a big corpus of words (e.g. Wikipedia) and using Wiktionary to parse it into word types (noun/adjective/verb). Then you could try to make a BNF syntax tree and see if it matches. You could use genetic algorithms to try to make a better syntax tree.
Historical OpenStreetMap view
Idea
Use the year_built tag in OpenStreetMap to make a map that you can have a slider that will show you what things looked like ages ago.
OpenStreetMap routing/directions based on passing a pub
Idea
The traditional Dublin way to give directions makes heavy use of pubs as landmarks (e.g. "Keep going until you pass The Clock, then turn right after the Ferryman" etc.). It would be cool to have a routing engine that gave directions based on this.
Implementation nodes
OpenStreetMap would be used as the data source, obviously. It could be done by building a state machine, where each state is "You are standing on section of street X". The location of pubs can be used to make the state machine state changes, e.g. "Turn left/right before/after pub X". Then it just becomes a matter of finding a path through the 'graph' of states.
If this was done purely based on pubs, i.e. you can only turn around a pub, you would probably have some very convoluted directions.
OpenStreetMap Data Cartogram
A cartogram is a map where ares/countries are enlarged or shrunk based on some attrivute other than area, e.g. population.
I'd like to make a cartogram where areas are enlarged based on the amount of data that's in OpenStreetMap for that area. This would be an interesting way to show areas where there is lots of OSM data