How to align rotated tick labels?

Similar to Szabolcs's and my answers here, I would suggest writing your own custom tick function, so that the labels are set into a Pane which can be both Rotated and have ImageMargins.

myTickList[min_, max_, seg_, shift_?NumericQ, phi_?NumericQ, len_: 0.01] := 
 Table[{i, Rotate[Pane[Style["y =" <> ToString[i], LineSpacing -> {0, 12}], 
     FrameMargins -> {{shift, 0}, {0, 0}}], phi], {len, 0}}, 
    {i, If[Head[seg] === List, Union[{min, max}, seg], 
    Range[min, max, seg]]}]

Examples:

fakedata = Accumulate@RandomVariate[NormalDistribution[0, 0.5], 40];

ListLinePlot[fakedata, Frame -> True, GridLines -> {None, Automatic}, 
 FrameTicks -> {{Automatic,  Automatic}, {myTickList[0, 40, 4, 25, Pi/4], None}}]

ListLinePlot[fakedata, Frame -> True, GridLines -> {None, Automatic}, 
 FrameTicks -> {{Automatic, Automatic}, {myTickList[0, 40, 4, 5, Pi/3], None}}]

Brett Champion posted a nice clean method in Labeling a bar chart, changing how rotated labels are centered that can be applied here as well:

center = Row[{#, Invisible[#]}, "\[NegativeThickSpace]"] &;

d = Range[10];

xticks = Table[{n, center @ Rotate["The y value is " <> ToString[n], 45 Degree]}, {n, d}];

ListPlot[d, Frame -> True, FrameTicks -> {{Automatic, None}, {xticks, None}}]