I have a lot of files uploaded with wp-admin in uploads folder. I don't have access to FTP, however, I need to download those files stored in uploads directory. Is there a way of doing it? Like - a wp plugin or something.
I'm not aware of any native function, or plugin that does specifically that task.
You could try a backup plugin, like Backup Buddy, which will create a full backup of your entire site (including uploads). You could then download and unzip the backup and extract specifically the uploads folder.
Backup Buddy is a paid for plugin, but I expect there are some free plugins that will do a similar job.
If you don't have access to FTP at all then you would not be able to install a plugin. Have you tried going directly to your uploads folder via your browser? Typical Wordpress sites use a path like "http://www.yourdomain.com/wp-content/uploads/". Once you are in the uploads folder you will see folders for each year and within these folders for each month. I know it is tedious but you can always download your content manually this way. If you are somehow able to install plugins without FTP then you might try this one as well, which is free: http://wordpress.org/extend/plugins/ftp-to-zip/
If you don't have access to FTP at all then you would not be able to install a plugin
Nonsense... Login as admin and you most definitely CAN install any plugins you want. This is the whole point of Wordpress.
Now, apart from said OP's mistake she does make a good point of pointing to your uploads folder and downloading it from there. This is assuming you don't have any strange permissions on the uploads folder.
Additionally, you could look into using wget. I've used it in linux to download an entire site but I'm sure there are similar options for windows... maybe curl?
If you don't have access to FTP at all then you would not be able to install a plugin.
iamthwee is right if the the /wp-content folder is writable AND your 'FS_METHOD' in wp-config.php is set to 'direct' AND your web username has permission to write to files/folders on your server. SSH is also an option, but I think Wget is the best suggestion. I will run on Linux and Windows. http://www.gnu.org/software/wget/