What is the longest word possible in Boggle? It turns out there are actually 31 of them. On a 4x4 board, there is only one 'qu' amongst all sixteen cubes so the longest possible combination is 17-letters (all 16 cubes with one 'qu'). Now you can debate whether adding -ness or un- really counts as a real word (let alone squirrelsstagnate!), but even Merriam-Webster agrees that inconsequentially is a word. Don't get your hopes up on ever finding it though; your chances are less than one out of 170 quintillion (10^18).
Here is a list of the longest possible words. I used the dictionary search from the National Puzzlers' League to find 17-letter words including the combination 'qu'. I wrote my own script to find whether forming a word was possible. It uses the actual 16 six-sided Boggle cubes and the numbers following the word are the necessary order of the cubes (numbered 0 to 15).
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| 0 | acquaintanceships | 4, 7, 15, 6, 3, 2, 0, 14, 13, 10, 12, 5, 1, 9, 8, 11 |
| 1 | consequentialness | 7, 3, 2, 5, 0, 15, 1, 4, 6, 9, 14, 12, 13, 11, 8, 10 |
| 2 | counterequivalent | 10, 14, 7, 2, 0, 1, 9, 3, 15, 5, 12, 8, 13, 4, 11, 6 |
| 3 | counterquestioned | 7, 10, 11, 2, 0, 1, 9, 15, 3, 8, 6, 5, 14, 13, 4, 12 |
| 4 | disequilibrations | 5, 3, 8, 0, 15, 7, 12, 9, 14, 13, 4, 1, 11, 6, 2, 10 |
| 5 | inconsequentially | 3, 2, 7, 10, 4, 8, 0, 15, 1, 11, 6, 5, 14, 9, 13, 12 |
| 6 | inquisitorialness | 3, 2, 15, 5, 8, 7, 0, 6, 1, 9, 14, 12, 13, 4, 10, 11 |
| 7 | nonquantitatively | 2, 10, 4, 15, 8, 11, 0, 3, 1, 14, 6, 7, 12, 9, 13, 5 |
| 8 | nonrelinquishment | 2, 14, 4, 0, 1, 9, 3, 11, 15, 5, 8, 10, 7, 12, 13, 6 |
| 9 | ovatoquadrangular | 3, 1, 4, 0, 6, 15, 8, 5, 9, 10, 11, 2, 7, 12, 14, 13 |
| 10 | overqualification | 3, 1, 0, 12, 15, 4, 13, 5, 8, 9, 7, 10, 6, 11, 14, 2 |
| 11 | oversqueamishness | 6, 1, 0, 9, 3, 15, 2, 14, 7, 5, 8, 13, 4, 12, 10, 11 |
| 12 | phenanthraquinone | 8, 1, 0, 2, 6, 4, 3, 10, 9, 14, 15, 5, 11, 7, 13, 12 |
| 13 | quadriarticulated | 15, 4, 5, 0, 3, 8, 1, 6, 9, 10, 11, 13, 14, 7, 2, 12 |
| 14 | quadricentennials | 15, 4, 5, 0, 3, 10, 1, 2, 6, 9, 11, 13, 7, 14, 12, 8 |
| 15 | quadricrescentoid | 15, 4, 5, 0, 3, 7, 1, 2, 8, 10, 9, 13, 6, 14, 11, 12 |
| 16 | quadrilateralness | 15, 4, 5, 0, 3, 9, 6, 7, 1, 12, 14, 13, 2, 11, 8, 10 |
| 17 | quadrituberculate | 15, 4, 5, 0, 3, 1, 7, 14, 2, 9, 10, 11, 13, 8, 6, 12 |
| 18 | quartermasterlike | 15, 4, 0, 1, 2, 9, 7, 14, 10, 6, 3, 12, 13, 5, 8, 11 |
| 19 | quartermastership | 15, 4, 0, 1, 2, 9, 7, 14, 3, 6, 11, 12, 8, 13, 5, 10 |
| 20 | quattuordecillion | 15, 8, 0, 1, 7, 6, 9, 5, 2, 10, 3, 12, 13, 11, 14, 4 |
| 21 | quintessentiality | 15, 3, 2, 0, 1, 8, 10, 4, 11, 5, 7, 14, 13, 9, 6, 12 |
| 22 | sesquicentennials | 3, 0, 5, 15, 7, 10, 1, 2, 6, 4, 11, 13, 9, 14, 12, 8 |
| 23 | squirrelsstagnate | 3, 15, 5, 0, 1, 2, 9, 8, 11, 6, 10, 4, 13, 14, 7, 12 |
| 24 | superadequateness | 3, 7, 8, 0, 1, 4, 5, 2, 15, 14, 6, 9, 13, 12, 10, 11 |
| 25 | supraquantivalent | 3, 7, 8, 0, 4, 15, 10, 2, 1, 5, 12, 14, 9, 11, 13, 6 |
| 26 | transequatorially | 0, 1, 4, 2, 3, 11, 15, 8, 6, 10, 9, 7, 14, 12, 13, 5 |
| 27 | unconquerableness | 7, 2, 10, 3, 4, 15, 0, 1, 6, 14, 9, 11, 13, 12, 5, 8 |
| 28 | unconsequentially | 7, 2, 10, 3, 4, 8, 0, 15, 1, 11, 6, 5, 14, 9, 13, 12 |
| 29 | uninquisitorially | 7, 2, 3, 4, 15, 5, 8, 9, 6, 10, 1, 11, 14, 0, 13, 12 |
| 30 | unquestionability | 7, 2, 15, 0, 3, 1, 5, 10, 4, 8, 14, 9, 13, 11, 6, 12 |