Realtime filtering on a microcontroller, with dynamic cut off frequencies
You can pre-compute the coefficients for a bunch (say $N=1024$) different cutoff frequencies. If your application doesn't need to provide fine control over the cutoff frequency, just read from your table and you're done. This works best if you have a lot of ROM and/or you use short FIR or IIR filters.
If you need finer control than those $N$ values, and if the relationship between your coefficients and cutoff frequency is well-behaved (ideally, monotonic), you can use linear interpolation within the pre-computed table of coefficients. This works best with well-behaved structures like state-variable filters - for which the coefficients are monotonic functions of the cutoff frequencies, and which do not get unstable when modulating them at fast rates. This is a very common problem in musical audio applications (equalizers, synthesizer analog filter emulation...). If you use other filter topologies, make sure that they cannot get unstable when their coefficients are changed "in mid-flight" - to me, this is a harder problem than actually computing them.