Here's a list of words in some Indian languages (mostly Hindi, Kannada and Tamil) that are derived from Sanskrit words (hence called tadbhava words). This list only contains words that are commonly unrecognized as tadbhava words, either due to a long series of changes, very unpredictable changes that make the connection to the original word unclear, or just simply because nobody has documented the words or paid attention. This list will be an active one, with words being added as and when I find or recollect them.
As a native or near-native speaker of these 3 languages, and having a linguistic talent for quickly learning new languages as well as analyzing origins of words, I can confidently verify to the authenticity of this list. I consider myself blessed to have had the opportunity to study Sanskrit early in school and thus get a firm foothold in Sanskrit literature. Not only is the study of the rich literature a source of bliss in itself, and a perpetual reason for intellectual, spiritual and aesthetic satisfaction, but it is always a thrill to discover a word in Sanskrit literature and make a connection to an obvious derivative (tadbhava) word in a vernacular language. The following list also shows that Sanskrit has always been a pan-Indian language from the earliest times and has influenced all languages, be they northern or southern. In fact, Patañjali the author of the great grammar commentary Vyākaraṇa-Mahābhāṣya mentions the variations of the verb 'to move' in different regions of India (udīcyeṣu - in the north, kambojeṣu - in the northwest, prācyamadhyeṣu - in the east and central regions, āryeṣu - in the central heartland, between the Sarasvati and Drshadvati rivers around Kurukshetra). He also mentions a characteristic of the Sanskrit spoken in the southern regions - "priyataddhitāḥ dākṣiṇātyāḥ" - "the southerners are fond of derivative descriptive words".
Any inputs from readers are always welcome. The format of the listing will be:
English meaning: Sanskrit word --> (any intermediate morphs) --> final word in the language
Hindi
1. Ox or oxen: बलीवर्दः balīvardaḥ --> (बइल्ला ba-illā Prakrit) --> बैल bail [I discovered this connection when I was reading Śūdraka's Sanskrit play Mṛcchakaṭikaṁ, which has one of the characters speaking in Prakrit and using the word ox. It then flashed across my mind that this is the derivation of the Hindi word.]
2. Stone or rock: प्रस्तरः prastaraḥ --> पत्थर patthara
3. Brick: इष्टकः iṣṭakaḥ --> ईंठ īnṭha
4. Black magic: यातु yātu --> जादू jādū [This connection was sparked when I was reading Vasiṣṭha's hymn in the Ṛg Veda 7.104.15 - adyā murīya yadi yātudhāno asmi, "May I die today if I am a black magician" which is a vow.]
5. Serpent/snake: सर्पः sarpaḥ --> साँप sānp
6. God (Krishna): कृष्ण kṛṣṇa --> कान्हा kānhā
7. Knot: ग्रन्थः grantha --> गाँठ gāṅṭh
8. Father-in-law: श्वशुरः śvaśuraḥ --> ससुर sasur
9. Mother-in-law: श्वश्रू śvaśrū --> सास sās
10. Daughter-in-law: वधू vadhū --> बहू bahū
11. Son-in-law: जामातृ jāmātṛ --> जमाई jamāī
12. Brother-in-law (wife's brother): स्यालः syālaḥ --> साला sālā
13. Sister-in-law (husband's sister): ननान्दृ nanāndṛ --> ननद nanad
14. Barren (earth or woman): वन्ध्या vandhyā --> बाँज bānj
15. Conversation/news: वार्ता vārtā --> बात bāt
16. Old (person): वृद्धः vṛddhaḥ --> बुड्ढा/बूढा buḍḍha/būḍhā
17. Sugar: शर्करा śarkarā --> शक्कर śakkar
18. Rain: वर्षा varṣā --> बरखा barkhā
19. Camel: उष्ट्र: uṣṭraḥ --> ऊँठ ūnṭha
20. Youth: युवन् yuvan --> जवान javān
Kannada
1. Brick: इष्टकः iṣṭakaḥ --> इट्टिगे iṭṭige
2. Festival: पर्व parva --> (पब्ब pabba) --> हब्ब habba
3. Color: वर्णम् varṇaṁ --> बण्ण baṇṇa
4. Flour: पिष्टम् piṣṭaṁ --> (पिट्टम् piṭṭaṁ) --> हिट्टु hiṭṭu
5. Money/currency: पणम् पण्यम् paṇaṁ/paṇyaṁ --> हण haṇa
6. Village: पल्ली pallī --> (पळ्ळी paḷḷī) --> हळ्ळि haḷḷi
7. House lizard: पल्लिका pallikā --> हल्लि halli
8. Town: पत्तनम् pattanaṁ --> पट्टण paṭṭaṇa
9. God (Brahma): ब्रह्म brahma --> बोम्म bomma [The 'o' is really a short sound in Kannada, and doesn't have an equivalent in Sanskrit which only has the long 'o' sound]
10. God (Krishna): कृष्ण kṛṣṇa --> किट्ट kiṭṭa [Of course, this is a more colloquial usage, but it does show how Kannada transforms the Sanskrit sounds.]
11. Lakshmi (wife of god Vishnu): लक्ष्मी lakṣmī --> लकुमी lakumi
[This is a more colloquial/rural usage, but also used in old poetry to adjust for rhyme or meter.]
12. Knot: ग्रन्थः grantha --> गण्टु gaṇṭu
13. Daughter-in-law: स्नुषा snuṣā --> सोसे sose
14. Sister-in-law (husband's sister): ननान्दृ nanāndṛ --> नादनी nādnī
15. Barren (earth or woman): वन्ध्या vandhyā --> बंजे banje
16. Conversation/news: वार्ता vārtā --> मातु mātu
17. This/that: इदम्/अदः idaṁ/adaḥ --> इदु/अदु idu/adu [In this case, the borrowing could be in either direction.]
18. Sugar: शर्करा śarkarā --> सक्करे sakkare
19. Bird: पक्षी pakṣī --> हक्की hakki
20. Cow: पशु paśu --> हसु hasu [Although the Sanskrit word means 'animal' in general, the cow has always been the animal par excellence in India.]
21. Zero: शून्यम् śūnyaṁ --> सोन्ने sonne
22. Sound/noise: शब्दम् śabdaṁ --> सद्दु saddu
23. Thousand: सहस्रम् sahasraṁ --> सासिर/साविर sāsira/sāvira
24. Riverbank: तट: taṭaḥ --> दड daḍa
25. Camel: उष्ट्र: uṣṭraḥ --> ओण्टे oṇṭe
26. Root: वेर: veraḥ --> बेरु beru
[ incidentally, the Sanskrit शृङ्गवेर: śṛṅgaveraḥ ("horn root") is the origin of the English "ginger"]
27. Tail: वालः vālaḥ --> बाल bāla
[ apparently वालः vālaḥ is itself a Prakritization of वारः vāraḥ because Yaska in his Nirukta explains वालः as "दंशवारणार्थम्" daṁśa-vāraṇārthaṁ, i.e. "used to get rid of biting insects (by animals)", so the root word suggests वारः vāraḥ as the original word]
Tamil
1. World: लोकः lokaḥ --> उलगम् ulagaṁ
2. Village: पल्ली pallī --> पळ्ळी paḷḷī
3. House lizard: पल्लिका pallikā --> पल्लि palli
4. Color: वर्णम् varṇaṁ --> वण्णम् vaṇṇam
5. Lord/Master: स्वामी svāmī --> चामी cāmī
6. God (Brahma): ब्रह्म brahma --> पिरम pirama
7. God (Krishna): कृष्ण kṛṣṇa --> कण्णा kaṇṇā
8. Sir/Madam: श्रीमान्/श्रीमती śrīmān/śrīmatī --> (तिरु) तिरुमान्/तिरुमती (tiru) tirumān/tirumatī
[The same transformation happens with Śrīpati - The Lord of Śrī - Lord Vishnu - Tirupati the world- famous Hindu temple of the seven hills.]
9. Fruit: फलम् phalaṁ --> पळम् paḷam
10. Thousand: सहस्रम् sahasraṁ -->(सासिरम् sāsiram)--> आयिरम् āyiram
