Since the question specifically refers to maps, I should mention that it is quite normal for it to appear that rivers run towards higher ground, such as hills or mountains, on a large scale map. This happens because on a large scale map you can't see the actual terrain the river flows through, which can be much lower than the average level of the area that you see on a map. The river can erode itself quite a deep canyon given time.

Two possibilities are obvious:

1. Water level used to be much higher due to an ice dam or similar and this forced water to flow through the high ground and erode itself a canyon.
2. The terrain used to be lower and has risen slower than the river can erode its channel. This can be due to plate tectonics or past glaciation.

While this does not quite answer the question as asked, I think there is some value in directly addressing the stated motivation for the question.

Since the question specifically refers to maps, I should mention that it is quite normal for it to appear that rivers run towards higher ground, such as hills or mountains, on a map showing only the large scale details. This happens because you can't see the actual terrain the river flows through, which can be much lower than the large scale features that you can see on the map. The river can erode itself quite a deep and narrow canyon given time.

Two possibilities are obvious:

1. Water level used to be much higher due to an ice dam or similar and this forced water to flow through the high ground and erode itself a canyon.
2. The terrain used to be lower and has risen slower than the river can erode its channel. This can be due to plate tectonics or past glaciation.

While this does not quite answer the question as asked, I think there is some value in directly addressing the stated motivation for the question.