If you can pick it up, you probably need it.
—
Holkins, Jerry; Krahulik, Mike (November 14, 2011).
"Thulsa Broom" .
Penny Arcade .
But seriously?
Unless it has no interesting value, leave them be.
You'll get one when you need one.
gaming.stackexchange.com/users/4815/Konerak
Some items that seem useless at first do have a hidden use.
For example, ruined books can be used to create summon Atronach
spell tomes
gaming.stackexchange.com/users/11240/Xenox
Once you learn Telekenesis
you can 'use' all objects as projectiles.
gaming.stackexchange.com/users/3610/fredley
Ruined books are used in atronach forge under the winterhold college.
The atronach forge provides a use for that "stupid" broom as well, actually!
gaming.stackexchange.com/users/17371/chris
To be quite honest, all items have a use... depending on your taste of Medieval living, you can decorate your house with whatever you deem worthy!
gaming.stackexchange.com/users/17786/Los Tha Don
Many of the items are useless or have very limited uses.
Everything could certainly be sold to merchants or used to decorate homes.
However, beyond that, the following list of things have no use Basket Bellows Bloody Rags Bowl Bucket Burned Book Candlestick Cast Iron Pot Clothes Iron Cup Drum Embalming Tool Empty Skooma Bottle Flagon Flower Basket Flute Fork (non-weapon) Goblet Hammer Inkwell Jug Kettle Key to Wintersand Manor Knife (non-weapon) Lantern Linen Wrap Lute Pitchfork Plate Platter Pot Quill Saw Shovel Silver Candlestick Soul Gem Fragment Spigot Spoon Tankard Tongs Torture Tools Troll Skull (Now actually can be used to build a trophy in your homestead) Wooden Bowl Wooden Ladle Wooden Plates http://skyrim.gamepedia.com/Useless_Items
As have been noted by the other answers/comments, all of these items could be used with telekinesis to create a projectile.
Furthermore, buckets could be used to cover shopkeeper's heads, allowing you to steal with impunity.
Beyond these items, many other items have very limited uses and are in general not worth picking up.
These include ruined books and brooms.
Most things labeled "clutter" would fall under the above two categories.
These items are in general not worth picking up.
If you ever find that you have a need for them, they are also easy to find.
gaming.stackexchange.com/users/176423/Fluidized Pigeon Reactor
Can every item in Skyrim be used for something? I find a lot of objects like ruined books, embalming tools, etc. that I haven't found a use for yet.
Is there a use for every item in Skyrim?
gaming.stackexchange.com
<the-elder-scrolls-5-skyrim>
gaming.stackexchange.com/questions/38405
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Some items that seem useless have a hidden use. For example, ruined books are used in atronach forge. All items can be sold to merchants. The use of an item can be interpreted differently by every player, thus every item technically has a use, but practically there are indeed items of no use.
The community explains that practically useless items exist.