Many db requests with relationship fields
This is how relationships work in Craft at the moment. Each relation equals +1 query. If you don't access your relation on an entry the query isn't executed. So by only fetching title and/or id you don't run any extra relationship queries.

Caching is your best option at the moment to make the query count go down. Make use of caching to cache large chunks of you code.

Brandon has hinted on Slack that Craft3 might incorporate Yii2 lazy loading of relations using the ->with() command. This will solve a lot of the N+1 queries with relationships.

Update

The release of Craft 2.6 included the functions for Eager-Loading of elements. See this link for documentation on the subject: https://craftcms.com/docs/templating/eager-loading-elements