Google Plus is a good image hosting website to consider among many other alternatives, such as Flickr, or even Facebook. I've just started to host some of my photos there and so far it's quite satisfactory.
Here are some thoughts and tips on using Google Plus for hosting images and videos.
Unlimited photo uploads
The service is free so there are some limitations.
Google+ users get unlimited uploads for images smaller than 2048 by 2048 pixels. Large images will be scaled down automatically. Images are compressed after uploading and the quality is quite good, visibly better than Facebook.
There's no tagging for photos although you can caption them. Captioning them is the only easy way to find them in the future. Imagine doing a search for "DCS1001.jpg" vs "Flea market on 10 Oct 2012".
You can create unlimited albums, but you can't create albums of albums. Number of albums can grow quite quickly and out of control.
Video uploads are quite generous
Video uploads are subjected to 15 minutes each, up to 1080P. There's a file size limit but I can't confirm the actual size — I tried uploading a 1GB file the upload page gave a "server timeout" error.
The videos can be downloaded by the public. To share them privately, you can specify an email address or Google Plus account — great for sending huge video files over the web.
Downside is the video cannot be embedded. To share the video, you have to share the URL link.
Certain features missing
There are no statistics. There's no data on how many times a photo/video has been viewed or downloaded.
There aren't a lot of embedding features. They don't give you BBCodes or HTML to embed photos as well. To share manually, you have to copy and share the URL.
It's not easy to find out how to set the visibility of photos/videos.
About embedding images
When you're on the image page on Google+, you can right click and copy the image URL and use that for embedding.
The link looks something like this below. Pay special attention to the part in the URL, between two slashes /, where numbers are followed by a "s". In the example below, that's the "s650".
That's the long side of the image, which is either the width or the height.
If you have uploaded a 2048 by 2048 pixel image, and you want to link that original size, just change that part of the URL to "s2048". If you want photos to fit into a blog's column, just adjust the number appropriately - I use "s500" for my blog.
Specifying the width of a vertical image is tricky because that method only changes the long side, which will be the height and not the width. So if you need to link an image to a certain size, just resize it appropriately prior to uploading. Or you can use the trick of adding this bit of HTML code width="500" to the img tag like the following:
<img src="https://.../.../.../s650/example.jpg" width="500" />