Plot[Sin[x], {x, 0, 10}, TicksStyle -> Large]


<img src="http://www.tri.org.au/TicksStyle.png">


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}}]


<img src="http://www.tri.org.au/ticksstyle2.png">