What would cause my furnace to only work with the filter removed?
As Tester101 mentioned (and he really should've made it an answer, because it's at least a partial one), the filter could restrict airflow to the point where your furnace overheats. Hence the 'Limit' error. 

But wait! Trying a cheaper filter, or running without a filter, isn't a good answer. You'll shortly find that the furnace won't run at all, with or without a filter. 

What this probably means is one of two things, both of which are not DIY in my book. The first is that your blower unit is going, or is clogged with dust/dirt/pet hair/warm fuzzies/etc. This would require a qualified HVAC professional to replace. The second is that you may have an A/C unit, and the coils are clogged. The second is somewhat DIY-able, but I can't give you directions because I don't know your unit. Mine slides out on kind of a tray, which lets me blow the coils off with compressed air or coil cleaner (which is available as an aerosol at the hardware or home improvement store near you.) 

Not tending to this risks a furnace fire. That's why it stops. Get it taken care of!