My favorite slice of life anime is Silver Spoon. It is a refreshing story about a farming high school.
Some others are (I suppose some of these could be labeled romance too):
- Usagi Drop (first season only - the second season just ruins it IMHO)
- Ore Monogatari
- Tonari No Kaibutsu-kun (this one actually has an ending if you want to read the manga to finish the story)
- Hanasaku Iroha
- Danna ga Nani wo Itteiru ka Wakaranai Ken (this show is only a couple of minutes per episode - but it so charming. The English is “I can’t understand what my husband is saying” - you have to watch all the episodes to appreciate it fully).
My daughter and I watch a lot of slice of life shows together so it is probably one of the reasons I enjoy them so much. I am sure I am forgetting some other good shows at the moment.