There are a number of vaccines in development of various different types. The NYT Vaccine Tracker is the place to keep track of all of them:
What are the ingredients?
Covid-19 vaccine excipients are too new to be included in the CDC’s Vaccine Excipient list, but those interested in frequently incorporated chemicals might find this list of interest:  In the UK, Oxford University posts information on common ingredients here:Vaccine ingredients
“WHAT ARE THE INGREDIENTS IN THE PFIZER-BIONTECH COVID-19 VACCINE? The Pfizer-BioNTech COVID-19 Vaccine includes the following ingredients: mRNA, lipids ((4-hydroxybutyl)azanediyl)bis(hexane-6,1-diyl)bis(2-hexyldecanoate), 2 [(polyethylene glycol)-2000]-N,N-ditetradecylacetamide, 1,2-Distearoyl-sn-glycero-3- phosphocholine, and cholesterol), potassium chloride, monobasic potassium phosphate, sodium chloride, dibasic sodium phosphate dihydrate, and sucrose.”
“WHAT ARE THE INGREDIENTS IN THE MODERNA COVID-19 VACCINE? The Moderna COVID-19 Vaccine contains the following ingredients: messenger ribonucleic acid (mRNA), lipids (SM-102, polyethylene glycol [PEG] 2000 dimyristoyl glycerol [DMG], cholesterol, and 1,2-distearoyl-sn-glycero-3-phosphocholine [DSPC]), tromethamine, tromethamine hydrochloride, acetic acid, sodium acetate, and sucrose.”
The FDA hearing on the Johnson & Johnson vaccine, a more traditional vaccine, will be held on 26 February. The ingredient list will be published if the vaccine is given Emergency Use Approval by the FDA. As of 22 February 2021, documents with might include vaccine ingredients have not been loaded onto the approval committee’s document page.As per the NYT Vaccine Tracker, the Johnson & Johnson candidate is a Viral Vector Vaccine and can be presumed to include ingredients common to that type of vaccine. Here’s how it works.
In India, the Serum Institute lists the Covashield Covid-19 ingredients:
“The BHARAT BIOTECH COVID-19 VACCINE (COVAXIN ) includes the following ingredients: COVAXIN contains 6µg of whole-virion inactivated SARS-CoV-2 antigen (Strain: NIV-2020-770), and the other inactive ingredients such as aluminum hydroxide gel (250 µg), TLR 7/8 agonist (imidazoquinolinone) 15 µg, TM 2-phenoxyethanol 2.5 mg, and phosphate buffer saline up to 0.5 ml. The vaccine (COVAXIN ) thus has been developed by using inactivated/killed virus along with the aforementioned chemicals.”
I think we’ve covered all the vaccines approved for use in the US and India as of February 2021.
Any other vaccine candidates?
The other candidates which are in different stages of trials in India to test safety and efficacy include:
ZyCov-Di, being developed by Ahmedabad-based Zydus-Cadila
A vaccine being developed by Hyderabad-based Biological E, the first Indian private vaccine-making company, in collaboration with US-based Dynavax and Baylor College of Medicine
HGCO19, India's first mRNA vaccine made by Pune-based Genova in collaboration with Seattle-based HDT Biotech Corporation, using bits of genetic code to cause an immune response
A nasal vaccine by Bharat BioTech
The Sputnik V vaccine candidate developed by Dr Reddy's Lab and Gamaleya National Centre in Russia
A second vaccine being developed by Serum Institute of India and American vaccine development company Novavax
These latter vaccines all show some promise, but have not been given any type of approvals as of February 2021 by either the US or India.