1. Logging out without sleeping on a bed will not remove your character in the map. Instead , your character would be in "stasis", with a matching indicator (similar of the Z's when AFK) that you're not in current control of your character. While logged out, your hunger and stamina bar is on hold, but not your SHP/HHP, plus you cannot SHP regen. You're protected from player assaults (except when summoned from scents), but not from wild animals.
2. Nightmares. Every time you log in from your bed, there is a small chance for some sort of "unfair penalty" bestowed upon you. It could be withheld item/equipment loss, SHP loss, temporary stat/skill loss, or jorb's horrendous doodles flashing for a few seconds before you could play.
3. Another function for dream catchers is to prevent "nightmares". Placing your bed within 5 tiles from a dream catcher should protect you.