The cheapest web hosting company for Pune is in the US.

No seriously, consider this:

• Why does your website have to be hosted in Pune? Most websites run by Punekars are running on hosts in the US and they're all doing fine. If you don't have a whole lot of traffic and a very fast and responsive site is not super-critical for your website, this is the best option.
• If most of your website visitors are in India, and fast+responsive is super-critical to you, then having a server in India is important. But remember, that is going to cost you quite a lot. You'll have to pay 2x to 4x more for having servers in India.
• Most "Pune" web hosting companies are simply reselling server space from hosts in the US. You can use http://WhoIsHostingThis.com to figure out where the actual servers are located. You're better off cutting out the middleman and going directly to the source.
• Anyone who claims "unlimited bandwidth, unlimited disk space" is lying.

(Note: hat tip to ankurp whose answer for best misal gave me the idea of "best X in Pune is actually outside Pune)

Aapkahost.com happy?

Cheapest is not always the best, there will be a lot of constraints if you opt for a free/cheap web hosting service I would suggest Fatcow.com for a good web hosting service, they offer unlimited bandwidth n disk space, plus a load of other useful services, and if you haggle a bit they'll reduce their price too

AapKaHost is really a good Company which is reliable and cheapest with the plans they have...

@Navin Kabra, This is not true for all hosts in Pune.

http://WhoIsHostingThis.com shows the owner of IP space , not the actual server/power/bandwidth owner.

Example, Leapswitch Networks Pvt. Ltd. (registered in Pune) owns and operates their equipment in Netriplex/UberBandwidth DC in Asheville, NC, USA. Now, as an Indian company, we cannot get IP space from ARIN without registering our company again in the USA.

So, except for the IPs, all server/network/power hardware is owned by us and sites hosted by us are shown as hosted by Netriplex LLC (owner of IP space)

GAJWEB is good web service company in pune, don't waste your time to search, just put request to Gajweb with your requirements, they will find which one is best solutions for you, your visit their home page at www.Gajweb.com or put message in their contact form, they will call you.