I'm also seeing this problem.  I can install any version up to 1.14 without running into this problem, but 1.14.0 through 1.14.3 produce this error.  Installs okay on my local test server.  Tried making the suggested PHP.INI changes (mysql.connect_timeout = 60, max_execution_time = 600, memory_limit = 36M) in my site's root (which does seem to override the Godaddy globals) but they made no difference.  I'm working with Godaddy on this and will post anything of interest.

My live site is on Godaddy:
PHP built On:  Linux p3slh113.shr.phx3.secureserver.net 2.4.21-53.ELsmp #1 SMP Wed Nov 14 03:54:12 EST 2007 i686 
Database Version:  4.0.27-max-log 
PHP Version:  4.3.11 
Web Server:  Apache 
WebServer to PHP interface:  cgi-fcgi 
Joomla! Version:  Joomla! 1.0.15 Stable [ Daytime ] 22 February 2008 23:00 UTC 

My test server:
PHP built On:  Linux lamp 2.6.20-16-server #2 SMP Sun Sep 23 19:57:25 UTC 2007 i686 
Database Version:  5.0.38-Ubuntu_0ubuntu1.1-log 
PHP Version:  5.2.1 
Web Server:  Apache/2.2.3 (Ubuntu) mod_python/3.2.10 Python/2.5.1 PHP/5.2.1 mod_ssl/2.2.3 OpenSSL/0.9.8c mod_perl/2.0.2 Perl/v5.8.8 
WebServer to PHP interface:  apache2handler 
Joomla! Version:  Joomla! 1.0.15 Stable [ Daytime ] 22 February 2008 23:00 UTC 

UPDATE: GoDaddy says they can't help with application problems, which they've clearly decided is the case here.  I asked them about MySQL settings, since other people on these forums are speculating that the problem is there.  Meanwhile, it seems to me that if I can install any version prior to 1.14.x with no problems, but nothing from 1.14.0 onward installs without this error, something must have changed in 1.14.0 that is causing this.  I think it would be great if an RSGallery2 developer would dig into this a bit to see if maybe a change that appeared in 1.14.0 is causing this and could perhaps be reworked.  Others have speculated that 1.14.0 is making some invalid assumptions about Joomla (i.e. that it's 1.5, not 1.0.x).  Failing that, some specific recommendations regarding settings would be helpful.  Thanks!

UPDATE: Godaddy says there are no MySQL settings that can be set by the user; they are all global.  If it turns out I need to change a MySQL setting to avoid this problem I'll be looking at changing to a different hosting provider.

UPDATE: I seem to have resolved this by making the following changes to my Godaddy root PHP.INI:
mysql.connect_timeout = 120 (previously tried 60)
max_execution_time = 600 (did this earlier to no effect)
memory_limit = 36M (did this earlier to no effect)
max_input_time = 120 (hadn't tried this before)

Not sure what fixed it but I'm happy anyway.

Interesting.  I hadn't noticed the template feature (silly me).  I had a look at the ones included and while none of them is particularly useful for my purposes, they do show what's possible.  Well, maybe it's time for me to delve into RSGallery2 template creation!

I can't seem to access any of the changelogs on the site.  I keep getting this "Feature only available in Debug mode" message.

I agree that the functionality of the frontend upload (My Galleries) is mostly the same as the backend, but as you say the interface is different.  From the user's perspective, the frontend certainly appears more complicated; there is simply a lot more going on than with the backend tools.

I don't have a problem with the My Galleries interface itself, since for some users it's the perfect interface to work with galleries and all types of uploads in one place.  What would be great, though, is a way to present a simplified interface to the user in the frontend, and certainly the backend upload tools would do the trick.  That way, I could add a direct link to this simplified upoad interface in my user menu while still allowing access to My Galleries for more advanced users.

There is also one nice feature of the backend upload that seems to be missing from My Galleries, namely the way you can keep adding more individual files in the single image upload interface by clicking the "more images" link.  This is very easy to understand for users.

I really like the backend upload tools.  Why not use them for the frontend?

There is apparently no easy way to provide front-end links to RSGallery2 functions, such as uploading images and batch uploading images. The only option seems to be to take the user to My Galleries, which is complicated from the user's standpoint. Interestingly, the back-end functions for upload and batch upload are clean and efficient, but access to them requires admin rights.

Ideally, the frontend user would click Submit Photos, be asked Single or Batch (may not even be necessary given the different filetypes (zip vs. pictures)), then dialogs similar to the back-end dialogs would continue. Also, the user should be asked if they want to put their photos in a new gallery (which would then be created automatically) or into an existing one, or possibly their uploads could be placed in a temporary folder prior to being approved by an admin (see below).

On a related note, there is no submit approval mechanism whatsoever. No approval required, no approval indicated, no email to admins.  From what I understand, this will be in a future version, which is great.

It also should be easier for an admin to see which images were uploaded by which user and at what time. Assuming an approval process, I would want to be notified that a user had uploaded some images, then look at a list of them, decide where to put them and move them accordingly.  Hopefully this will be included when the approval process is added in a future version.