We have about 5,000 JPG & PNG images. Each image has the size of 50KB - 100KB. We are currently using about 1TB - 3TB of bandwidth per month on our existing host but the cost is getting expensive.
We have thousands of users accessing (downloading) the images on our Google TV app and we would like help to find a solution / company that is reliable and cheap without any bandwidth limits. Any suggestions will be helpful, thanks in advance!
HostGator is (primarily) hosting websites, don't be surprised if you're using them for file storage and are getting a crappy service out of it.
Like the replies above said, a CDN is the way to go. I haven't used CDN77 so I couldn't tell you about it, but I can recommend AWS Cloudfront as a CDN, or at the very least AWS S3 for cheap file hosting. You only pay for the storage you've uploaded/bandwidth you've consumed, so you're not paying for wasted resources unlike some of the other CDNs you'll find.
If you decide you don't want to waste your time with a CDN you can go with the dedicated server route. OVH's montreal servers have a great price, and would be decent for a file server: 2TB storage, i3, 8GB RAM, DDoS protection, 5TB transfer for $40/m.
You're primarily serving static data with no 'website' as such, so you don't need a VPS or dedicated server. However, shared hosting is also unsuitable for you because the stresses of serving so many images will cause you to be a 'bad neighbour' and most shared hosts will either cut you off altogether or put you on a slow server out of the way so you don't bother others. Just pretend shared hosting plans with huge or unlimited bandwidth allowances don't exist, they're not geared towards your needs and you will run into performance/outage problems.
What you need is a CDN, which is specifically designed for serving static files such as images. Not only will it likely work out cheaper at such high volumes, but your users will experience much better performance because a CDN will serve the images from a local server.
Here are some to get you started, all of which I've tried and found the performance to be good:
CDN77 (OnApp CDN, free trial)
CDN.net (OnApp CDN, free trial)
Fastly (SSD CDN, free trial)
Speedyrails (EdgeCast reseller)
A whole bunch of CDNs have started appearing during the past few years that cater to relatively small usage like yours, driving prices down and providing flexible models. I'd look at all of the above and see which model works best for you.
FWIW, I don't rate the performance of Amazon CloudFront highly. Virtually every other CDN I've tried has been faster.