For anyone who's curious, here is the list of ALL problems solvable in BF - that is, every problem in this list has at least one solver in BF. The problems are sorted in decreasing number of solvers.
Sorry to site managers (I wrote a simple web crawler to get this list, so there may have been a peak in the incoming traffic to the server.)
Enjoy Brain-f**king 
Classical:
- CRYPTO321 (20+ solvers)
- BFTAB9 (20+ solvers)
- MULTIPLY8 (20+ solvers)
- CRYPTO26 (20+ solvers)
- SBSTR112 (20+ solvers)
- EDIT17 (20+ solvers)
- SORTING8 (20+ solvers)
- TEST6 (20+ solvers)
- BFTRI3 (20+ solvers)
- GALAXY5 (15 solvers)
- ADITYA133 (7 solvers)
- FAST_BF3 (5 solvers)
- BFMUL3 (4 solvers)
- PUCMM0091 (4 solvers)
- BFPRMCYC4 (3 solvers)
- BFREGEX13 (3 solvers)
- BFDIV6 (3 solvers)
- NGM2 (3 solvers)
- AMR12D (3 solvers)
- BISHOPS1 (2 solvers)
- ADDREV2 (2 solvers)
- FCTRL52 (2 solvers)
- HUBULLU1 (2 solvers)
- DOJO1 (2 solvers)
- SQUA_REV1 (1 solver)
- CUBES (1 solver)
- WSCIPHER (1 solver)
- GLOVE (1 solver)
- AMZRCK (1 solver)
- FCANDY2 (1 solver)
- WORDCNT (1 solver)
- THEPOOL (1 solver)
- AMZSEQ (1 solver)
- WILLITST1 (1 solver)
- GNY07H (1 solver)
- LASTDIG21 (1 solver)
- STPAR2 (1 solver)
- FCTRL1 (1 solver)
- NSYSTEM1 (1 solver)
- EIGHTS2 (1 solver)
- BFBASE4 (1 solver)
- TOANDFRO3 (1 solver)
Challenge:
- HS09BF5 (20+ solvers)
- LIB4 (20+ solvers)
- BFBIGTHN3 (20+ solvers)
- BFWRITE2 (20+ solvers)
- TSET1 (20+ solvers)
- BFMODULO4 (11 solvers)
- EVAL3 (10 solvers)
- PIVAL1 (10 solvers)
- CTQUINE1 (8 solvers)
- PRIC1 (7 solvers)
- MODULUS23 (7 solvers)
- KAMIL (4 solvers)
- XMAS (4 solvers)
- SQRT21 (3 solvers)
- BFSTR12 (3 solvers)
- SIZECON1 (3 solvers)
- TMBOX2 (2 solvers)
- FAST_BF22 (2 solvers)
- TSSTR3 (1 solver)
- ZRELY11 (1 solver)
- JCROSS2 (1 solver)
- DISPLACE2 (1 solver)
- XWORDS (1 solver)
- BFK_AUTO2 (1 solver)
- REVINPUT1 (1 solver)
- NOP1 (1 solver)
- POLYBIUS (1 solver)
- RIS1 (1 solver)
Partial:
- BGEEK2 (20+ solvers)
- PSAFAC2 (3 solvers)
- PT07I1 (2 solvers)
- SYMORD1 (1 solver)
- MST2 (1 solver)
- SBRICKS21 (1 solver)
Tutorial:
- MB22 (20+ solvers)
- FSTCHAR (20+ solvers)
- HELLO1 (20+ solvers)
- QWERTY022 (19 solvers)
- ASCII12 (17 solvers)
- QUINEI3 (9 solvers)
- VOWELS1 (2 solvers)
- MIRRORED (2 solvers)
- EMP (2 solvers)
- BCHARD1 (2 solvers)
- AMR11G (2 solvers)
- ADUN (2 solvers)
- BFBINADD1 (2 solvers)
- PWAD (2 solvers)
- HELLOKIT (2 solvers)
- DAYOUT2A (1 solver)
- FUACM003 (1 solver)
- BITCNTR (1 solver)
- DOUGHNUT (1 solver)
- NAJA (1 solver)
- BNUMBERS (1 solver)
- PAINTPOI (1 solver)
- SODUJ1 (1 solver)
- FUACM005 (1 solver)
- RLDEC (1 solver)
- LOOKSAY (1 solver)
- GNY07A (1 solver)
- FACTBASE (1 solver)
- TESTXOR (1 solver)
- FIBEASY1 (1 solver)
- EXFOR (1 solver)
Basics: