Do any goddesses have ten arms?

 Adi Para Shakti supreme goddess Maa Durga in her Katyayani Durga/Mahishasura Mardini form has ten arms where she killed the buffalo demon Mahishasura. See the following image:

This Katyayani Durga Mahishasura Mardini form of supreme goddess Maa Adishakti Durga is the one which we see in the Durga Puja pandals mostly and also in many temples of Maa Durga because this Katyayani Durga form of Maa is highly prominent in Sanatan Dharma. Even one of world's top 5 biggest temples Sri Adya Katyayani Shaktipeeth Chattarpur Temple, New Delhi also is dedicated to Katyayani Mahishasura Mardini form of Maa Adishakti Durga. See the inside images of that temple:

So beautiful and divine!

The above two are the images of Sri Adya Katyayani Shaktipeeth Chattarpur Temple which is one of the top 5 largest temples in Sanatan Dharma.

However the original swaroopa of the supreme goddess Para Shakti Maa Durga is with 8 arms mostly or sometimes with 4 or 2 arms.

Glory to the Supreme Goddess Para Brahman Ultimate Reality! Om Shakti. jai mata di

Vishnu has 4 arms and holds 4 objects. What are those objects?

 The four objects in the 4 arms of Vishnu are Shankha, Chakra, Gada, Padma or in simplified English equivalents they are Conch, Discus, Mace and lotus.

Now, which arm of Vishnu holds which object? That is an interesting question. The Dwaita philosopher Madhvacharya lists out 24 ways ( i.e. 4X3X2X1) of holding these objects in 4 arms, in his Tantrasara Sangraha. Accordingly, each form (Roopa) holding the objects in a specific way is given a name and worshiped for a specific purpose. These 24 forms (Roopa) are

1. Keshava : Shankha, Chakra, Gada, Padma (clockwise starting from the top right hand)
2. NarayaNa: Padma, Gada, Chakra, Shankha
3. Madhava: Chakra, Shankha, Padma, Gada
4. Govinda: Gada, Padma, Shankha, Chakra
5. VishNu: Padma, Shankha, Chakra, Gada
6. Madhusoodhana: Shankha, Padma, Gada, Chakra
7. Trivikrama: Gada, Chakra, Shankha, Padma
8. Vaamana: CHakra, Gada, Padma, Shankha
9. Shreedhara: Chakra, Gada, Shankha, Padma
10. Hrsheekesha: Chakra, Padma, Shankha, Gada
11. Padmanaabha: Padma, Chakra, Gada, Shankha
12. DaamodaraL Shankha, Gada, Chakra, Padma
13. SankarShaNa: Shankha, Padma, Chakra, Gada
14. Vaasudeva: Shankha, Chakra, Padma, Gada
15. Pradyumna: Shankha, Gada, Padma, Chakra
16. Aniruddha: Gada, Shankha, Padma, Chakra
17. PuruShottama: Padma, Shankha, Gada, Chakra
18. AdhokShaja: Gada, Shankha, Chakra, Padma
19. Narasimha: Padma, Gada, Shankha, Chakra
20. Achyuta: Padma, Chakra, Shankha, Gada
21. Janaardhana: Chakra, Shankha, Gada, Padma
22. Upendra: Gada, Chakra, Padma, Shankha
23. Hari: Chakra, Padma, Gada, Shankha
24. KrShNa: Gada, Padma, Chakra, Shankha

Following image shows the 24 ways in which Udupi Krishna - the Krishna installed by Madhvacharya at Udupi - is decorated to illustrate the 24 forms of Vishnu as explained above.