An obvious place to start is in the field of electronics. Computer-based tools are already used to build such stuff, so it's a natural replacement, right? Well, almost. There are tools for handling VHDL, Verilog and SystemC. There are frameworks for simulating both clock-based and asychronous circuits. You can do SPICE simulations, draw circuit diagrams, download existing circuits as starting points or places of inspiration, simulate waveforms, determine coverage and design PCBs. OpenCores provides a lot of fascinating already-generated systems, SUN provides the staggering T1 and T2 UltraSPARC cores, and the Sirocco 64-bit SPARC. This field has probably not got anywhere near what it needs, but it has a lot.
Maths is another obvious area. Plenty of Open Source tools for graphing, higher order logic, theorum provers, linear algebra, eigenvalues, eigenvectors, signal processing, multiple-precision, numerical methods, solvers for all kinds of other specific problem types, etc.
What about astronomy? That requires massive table data crunching, correlation of variations, moving telescopes around with absolute precision - things computers tend to be very good at. There are a few. Programs for capturing images are probably the most common, although some telescopes provide software for controlling telescopes, obtaining data and performing basic operations. Mind you, how much more than this does one need in software? Some things are better done in hardware (for now, at least) because the software hasn't the speed. Yes, the control software seems a little specialized, but it'd be hard to make something like that general-purpose.
Chemistry. Hmmm. Lots of trivial stuff, more educational than valuable - periodic tables, 3D models of molecules, LaTeX formatting aids. There's a fair amount on the study of crystals and crystallography, which is as much chemistry as it is physics, but there's not a lot else. Chemistry involves a lot of tables (which would be ideal for a standardized database), a lot of mathematical equations, formulae, graphing, measuring and correlating all sorts of data, the consequences of different filtering and separation techniques, the wavelength and intensity of energies, analysis of the results of atomic mass spectrometry or other noisy data, etc. I see the underlying tools for doing some (but not all) of these things, but I don't see the heavy lifting.
Archaeology has very few non-trivial tools. Some signal processing for ground-penetrating RADAR, but there are virtually no tools out there that could be useful for helping with interpretation. In fact, most RADAR programs don't interpret either but display the result on a small LCD screen. Nor do any tools exist for correlating interpretations (other than manually via an extremely naive - for this purpose - GIS database). There's a few scraps here and there, but signal analysis and GIS seem to be about it, and those were mostly developed for mining companies and tend to show it.
Biology has plenty of DNA sequencing code. By now, Slashdotter should be able so sequence eith own DNA, not pay someone a thousand to do it. You mean, those aren't enough, that you need more hardware? And a lot more software? It's an important step, but it's not unique.
Mechanical Engineering. I haven't seen anything of any significance.
Geology. Not really, beyond the same software for Archaeology, but using it for find seams in rock.
Sports: Lots of software getting used, but little of it is open source.
Result - those who gain with the least to lose and the most to win make the change. Those who feel like there's no benefit from changing what they're doing will continue doing what they're doing. My suggestion? There are gaping holes in Open Source. Fill them in.