Sad Songs from Umineko no Naku Koro ni and Higurashi

Umineko no Naku Koro ni has many good sad songs. The story of this visual/musical novel is very sad and melancholic. It deals with desperation due to overwhelming circumstances.

Wingless

The saddest of them all, possibly. However, nothing touches you as much as this one.

Soul of Soul is airy and soft. It is more dreamy than sad.

Worldend has a sense of conclusion to it, but also briefness and conclusion: sense that it is finally over. It is good for reflecting about what has happened. 

Fortitude - the name speaks for itself. Game plays it a lot and it easy to get tired of it as you play. However on its own, it is a very good piece. I gives you strength to go on.

7 Weights - This one has sence of urgency in addition to reflection Its melody is uniquely sophicticated.

Ricordando il Passato - similar in its conclusive nature to Worldend, but soft and gentle instead of brief. A lullby even an stressed ot adult can sleep to.

Oh, Desire by Jimang

This is opening for the Umineko anime is nor part of visual novels, but I think it is great fit for the franchise. It helps to summarize it.

Higurashi no Naku Koro ni

The first opening to Higurashi is mostly a suspense then sadness. However, this song can let you feel the underlying sadness of the characters, that drove them towards these extremes.

You can check the rest of the Higurashi soundtrack here, it is mostly sad. The very first song of this collection, simply called Main Theme reflects sadness and mistery really well.