If you can’t easily see the pattern of each series you may have too many.
Separate legends are the worst-case scenario in the line chart world. Often one can find the legend below the chart, or in an arbitrary order. You want to allow instant identification of the lines, but forcing the viewers to look them up in a legend takes way too much time. Instead you should put the labels somewhere close to the lines.
The great side effect of putting the labels next to the lines is that you no longer depend on fancy colors or disturbing symbols to identify individual lines. Extra points for simplicity.
If you are using different line styles you may be emphasizing some series more than the others; make sure that’s consistent with your users needs.
Sometimes you hear the advice that every (line) chart should have a baseline of zero, otherwise it would be “lying”. As a counter-example, here’s sales using baseline zero.
However, to minify the risk of confusing the readers with a non-zero baseline chart, I suggest to not draw the axes as connected lines. This way the y-axis doesn’t visually ‘touch’ the ‘ground’.
For example, if you have data for years 1980, 1990, 2000 and 2008, the spacing between 2000 and 2008 should be smaller than between other dates; if you can’t do it with line charts use a scatter plot.