Ley lines and dowsing are two very different topics with a very large difference in number of studies made.

Ley lines:
(1) I don't think Bert's idea (Roman roads) is viable except for very local patterns. Reason: Roads follow the principle of minimum energy and that only locally and in rare cases leads to straight lines. Possible objection: When did the military ever care about minimal energy when building a structure?
(2) I like more Scotsbard's idea (cleared paths for signalling), for that better explains the straight lines. Is there any evidence for that?
(3) An alternative explanation is that there are no more straight lines than can be expected by chance alone. Humans tend to see patterns in randomness, so that would explain why they were postulated in the first place. I know of no study that has tried to compare the number of ley lines to chance occurence (please tell me if there has been one). Perhaps this has not been done because it is difficult to find a chance baseline. You could do something like trying to draw straight lines in maps with all slate quarries in Germany, all coal mines in Poland, railway stations in Italy, pubs with folk music in England and so on. And if the percentage of straight lines in the ley line maps is significantly higher than in the other maps you'd say there is a case awaiting explanation. With the information I have so far it still is a case of 'no evidence yet'.

Dowsing:
List of links conveniently separated into Pro and Contra in case you'd prefer only to read from one side.
There have been many studies of dowsing, more or less well controlled, so this is a case where there is no need to say 'no evidence' from a scientific point of view.
The subjective and objective effects are strong and real and extremely convincing. The main dispute is about the interpretation. Penny has pointed out what the explanation most scientists agree with is: ideomotor movements (Carpenter effect).
The only possibility to test this interpretation against the interpretation that the movement comes from a force outside of the dowser are double blind experiments. All experiments of this type I know of have failed to find better than chance performance with one notable exception. A study by a physics professor in Munich claims to have shown extrachance hits. This study however has serious statistical problems that invalidates it in the eyes of most experts.
So the evidence at this point is that if dowsers do not know where to look, they are not better than chance. That of course doesn't at all exclude Penny's explanation: better than average ability to read the landscape, but it excludes the usual reasons dowsers give for their performance. The many field studies in a real environment have a lot of problems: what is the chance baseline? what are the controls? In too many cases there is no control group at all whichmore or less invalidates the results.

Wolfgang