Plot[Sin[x], {x, 0, 10}, TicksStyle -> Large]
For something not quite so big, use: Larger, or choose your own font size with:
Plot[Sin[x], {x, 0, 10}, TicksStyle -> Directive[FontSize -> 16]]
Edit: Further to @YvesKlett helpful comment, one can even choose different styles for the x and y axes:
Plot[Sin[x], {x, 0, 10}, TicksStyle -> {{FontSize -> 16, Orange}, {FontSize -> 22, Green}}]
