Can I upload files on blogspot ?

You can only upload image files to blogspot (blogger). For other types of file you must find your own hosting.

There is a limit of 300MB on the images you are uploading to a BlogSpot blog.

For non image files (for example css, javascript...) you can use one of the following services.

Free hosting services :

OpenDrive - in this moment in my opinion this is a best choice.
OpenDrive have 5Gb free space storage and bandwith of 1Gb per day. You can use OpenDrive service to host javascript files with javascript functions which you can call from your blogspot posts as an external javascript file.

First you need to sign in on this service
after you are signed in, go to files tab
under Files tab is a Upload option with which you can easily upload files from your computer to OpenDrive service
after file is uploaded you can see uploaded file inside MyDocuments in OpenDrive
when you hover your mouse over uploaded file there is a little arrow in upper right corner, when this arrow is clicked you can choose Links
in Links screen you can find:
- Direct link - this is a link you can choose for include javascript files in blogger post
- Direct link - link for direct download

Google groups

Unfortunately, Google groups no longer support upload of files. They remove the ability to upload new files to groups since 2011.
Create your own Google Group and upload files (100 MB).

First go on Google Group and sign in
Create group (clik on Create group as in picture below)

Name your group, write a group description and choose access level and click button "Create my group"
Now you can upload files

Click browse and choose file to upload from your computer
When you uploaded file, you can click on uploaded file in the list and in the address bar you will see url of hosted file

Now you can use this url in your code, for example:
view plain print ?
1. <link href='http://intblogsupport.googlegroups.com/web/SyntaxHighlighter.css?hl=en&gsc=LopFqhYAAAAyJt7F9v8L6AePkQCcpD2ug-kXU5InE09W2o0GCSVgCQ' rel='stylesheet' type='text/css'/>
if javascript file was uploaded and you want to use uploaded javascript use this code:
view plain print ?
1. <script src="http://everything-about-blogging.googlegroups.com/web/TestJs.js?hl=en&gda=bUe-djsAAAATLYFRxG7MFqGWBWh2VvtrqIEbF7jzfKsOTBbDD3S6g8oRXZrtFiBTuJ69H91AzQAGRdr3QrylPkw2aRbXD_gF&gsc=CJY8-AsAAABni9lzDVHuoDw_bqXODZJz" type="text/javascript"></script>

SkyDrive

Skydrive is online service which offers 25 GB of free online storage.
For hosting files and use them from your blog you must use little hack.
Unfortunately, this is working only 24 hours. After 24 hours URL (address) is changed.

You must have Windows Live ID to use skydrive, if you don't have, you can register
First upload file in public folder
Go to public folder on skydrive
Click on file you want to use in your blog
Right click on icon for download file and choose "Open link in new tab"