I am not a singer and I'm not a huge fingerplay person so I have found it challenging to find a way to successfully and succinctly end a storytime. Other than songs and fingerplays, what is an effective way to bring storytime to a close?
Songs and fingerplays are, of course, classic and effective storytime closers. But! If those aren't your thing, here are some thoughts:
Music: You could play a recorded song. Kids could be encouraged to dance or to follow the motions in the song, or it could simply be relaxing lap time. When the music is over, storytime is over.
Stamp or sticker: Sometimes I end storytime with a hand stamp (or sticker). This gives the kids an opportunity to practice the skill of forming a line (useful later in school) and gives me a chance to chat briefly with each child.
Bubbles: Some folks finish by blowing bubbles. This is especially popular with 2- and 3-year-olds. To avoid a stampede, it can be helpful to form kids into a circle and blow bubbles toward each child. Some people sing "Goodbye Bubble" during this (it helps create a sense of ending, especially when the song stops), but you could skip the song, simply speak the words, have the parents sing it, or play a recorded version. (To the tune of Frere Jacques: Goodbye bubbles, goodbye bubbles; Time to go, time to go; I will help you, I will help you; With a blow, with a blow.")
Toys, scarves or activities: Some storytimes end by transitioning into a free play period, sometimes with coloring sheets, crafts, toys, or scarves to play with. I like what MariBar said about this allowing time for us to interact with families.
Rhyme: What about a closing rhyme that is not a fingerplay or song, but simply spoken? A search for "storytime closing rhymes" (or "storytime opening closing rhymes") turns up a variety. (You don't care for fingerplays, but do you mind action rhymes that involve larger motor skills like clapping or patting one's knees? Just establishing a rhythm with their bodies tends to gather the kids' attention and create a sense of ritual.)
Ritual: I think the main thing is to create a sense of ritual, so that children recognize a familiar cue that storytime is about to end. Everyone could wave goodbye; you could sound a gong or ring a bell (or all the kids could); you could all pretend to go to sleep; you could review together the storytime's highlights (good for reinforcing narrative skills) and then all declare "Ta-da!" ... anything!
It very much depends on the age group (and somewhat on your resources), but I've always been involved in storytimes that end with a craft. You end the story then propose the craft as it relates to the story and provide direction in creating the craft; then everyone can work at their own pace and leave when they need to. I usually take the craft time to wander around and interact with the children and their caregivers: reinforcing skills, referencing the story and building relationships.