So one of my players is playing a kleptomaniac thief who just likes to steal stuff randomly (from locales, not from PCs). I was wondering if anyone had any good roll tables we could use, I'm not sat there trying to think of what they've managed to pinch this time. Ideally stuff that's interesting and flavourful, but not impactful on the game.

The trinket table in the PHB comes to mind, and any of the loot tables from the DMG if you're feeling generous, especially the non-magic items. Then there's also random item generators online. 5e Magic Shop lets you customize the input pretty well. 

There is a trinket table in the Player's Habdbook Equipment - Player's Handbook - Sources - D&D Beyond (dndbeyond.com) 

There is random treasure table in the Dungeon's Master Guide Treasure - Dungeon Master's Guide - Sources - D&D Beyond (dndbeyond.com)

There's also a trinket table in Icewind Dale: Rimes of the Frostmaiden adventure. Appendix A: Icewind Dale Trinkets - Icewind Dale: Rime of the Frostmaiden - Sources - D&D Beyond (dndbeyond.com) 

There is a random giant trinket table in Storrm King's Thunder adventure SKT_Items_in_a_Giant_Bag.pdf (wizards.com) 

I often search the net for the same kind of table when i want to generate random treasure table from giants, ogres, orcs and other barbaric humanoids.

The trinket tables are good for most of the time, also, maybe throw in a couple silver pieces sometimes, or use the stuff from the UA kender, maybe. But sooner or later, they’ve got to steal some macguffin from a villian and kick off a side quest, right? Like the gem they need to complete the ritual, or the scroll describing what the ritual is, or the secret, coded message about the plan to kill the king. I wouldn’t do it more than 1 or 2 times in the whole campaign, but seems like it’s just begging to be done at least once. The character just has to get bit by this.

Look through the equipment list for stuff without a price (like string or a small knife) or for stuff with low prices (like a piton or sling bullets).

You could also go for stuff with personnal aspect, family portrait, herloom, pins,  signet ring, badges, letter, seal stamp, name tag, and other mundane stuff such as nuts, dry fruits, perfume, chamber pot, drape, curtain, tent canvas, metal wire, piece of fiber, dead mouse, fork, spoon. music partition, instrument string, buckle, boot lace, shirt button, 

Things that could potentially launch into a tiny adventure...

• keys,
• prized heirlooms,
• sentimental object that its owner would want returned,
• cursed objects,
• soul trapped/trapping object,
• letter of an upcoming event
• letter from an influential person
• letter from a loved one or family member
• a previously stolen object wanted by a third party
• rare collectible
  • coin
  • doll
  • teapot

I use Kassoon for on the fly treasure generation by CR. It provides a handy list of trinkets with each list generated; Treasure Generator - Kassoon.com

I played a barbarian once who was the same way - he'd walk through a market and just randomly grab stuff, apples, candles, pastries, whatever. The GM and I agreed that so long as none of it had any real value, and no real use, we didn't need to roll for it. Not what it was, and not whether anyone noticed. 

This worked wonderfully. And we had a lot of fun with it. Borgrim (for such was his name) would carry around a sackful of random snacks, and a bag of totally random items that I could decide at a whim - so long as they weren't affecting the game in any meaningul way. A horseshoe, a hinge, half a deck of cards, a rabbit pelt, whatever. 

Of course, when he stole the rubies set in the eyes of a statue of a major goddess in the cathedral of the capital city, that was different. But then he fashioned them into earrings for his possible future girlfriend - again negating the need for assigning value to the things.

Here's some items I've added to random loot tables, or a rare treat if someone rolls a natural 20 on a Sleight of Hand skill check (in addition to what they'd already receive):

1. A broken psionic screwdriver.
2. A neutron flow polarity reverser.
3. A bullet with the name 'Baldrick' etched upon it.
4. A torn-off piece of paper with the number '42' scribbled upon it.
5. A tiny pouch of vraxoin.
6. A key with a label attached: "to close shut the drawers of Oblivion."
7. A broken water chip, whatever one of those is.
8. A tiny box with some sort of fine ribbon running through it, with the words "Blind the Wind" written on it.
9. A pocket abacus with a label attached: "can it run Doom?"
10. A brass badge depicting an eagle behind a shield. Emblazoned on it is the word 'DREDD'.
11. A business card for Quitters, Inc.
12. A rolled up painting titled "The Road Virus Heads North." You swear it's getting closer each time you look at it.
13. A pair of goggles that make you see the cynical intent of propaganda posters in black-and-white.
14. A complete set of left-handed cutlery.
15. A locked jewellery box, holding only its key. 
16. A pouch of gold dust. As you take it, you notice a figure in a full suit of silver armour become startled, and make its retreat.
17. A bloodied spearhead. Whilst holding it you can hear an angelic choir, even if you are deafened by any means.
18. A pocketbook which names all who will enter Heaven. Everyone in the party's name appears in it except the first person who reads it.
19. A rune with the letter 'M' for 'Mini', which can be turned upside-down (or downside-up) to 'W' for 'Wumbo'. You are granted expertise in Wumbology whilst the rune is set to Wumbo.
20. A bottle of Mepsipax, the drink of choice for scarecrows. In return for this drink, scarecrows will answer a single question the party poses them.