I'm hoping to do some development work on Altera FPGAs that will likely be larger than is supported by the free edition of ModelSim. I have an old copy of the full version hanging around (version 6.5, I think) -- is this likely to work for designs with modern FPGAs (e.g. Cyclone IV), or do I need to upgrade?
Well theoretically it should work, the only thing you need to do is to compile your libraries in modelsim. One thing I don't understand is why do you think your files would not work with modelsim? Is it because you are using Verilog 2001 or syntax that is not supported? As long as your code is written in high level language like verilog and VHDL, you will be able to fix it so it can work with older version of Modeslsim.
If you are not using any vendor-supplied cores, then it doesn't matter what device you are using. As long as the VHDL you write is supported by the old tool, you should be fine.
If you have vendor cores, then as long as you have the source to any cores you are using and can compile them in the old tool (which is likely as most vendor cores only use VHDL-93) there should be no problem there either.
Device specifics matter a lot more in synthesis than simulation.
Watch out if using Altera QSYS for system assembly, the generated interconnect uses some SystemVerilog which will probably not be supported by MSim 6.5.
The latest version of Quartus web edition is free. http://www.altera.com/products/software/quartus-ii/web-edition/qts-we-index.html I doubt your version of Modelsim will work with any of the Cyclone series.