Rebuild icudt51l.dat file?
Another solution for this is to boot into your recovery partition with CMD+R while your machine is booting. From there you can open the Terminal from Utilities in the menu bar. Then you can copy the file with:
cp /usr/share/icu/icudt51l.dat /Volumes/YOUR_DRIVE/usr/share/icu
If your drive has FileVault enabled you may have to unlock that through disk utility first.
In Terminal with developer tools installed I ran the commands:
curl -O http://download.icu-project.org/files/icu4c/51.2/icu4c-51_2-src.tgz
tar xvf icu4c-51_2-src.tgz
cd icu/source
rm -rf data
./runConfigureICU MacOSX --with-data-packaging=archive
make
and from data/out
I copied icudt51l.dat
to /usr/share/icu/
.
Apps now seem to run fine again, but it would seem some caches got deleted.