Organizations which don't foster this kind of relationship are really short changing themselves. Some of those junior people turn into stellar contributors in short order, and without a little guidance would have been frustrated and lost.
As a senior guy I feel vastly more productive and interested spending half my days in a series of little one-on-ones and in depth reviews then just burping out features with my headphones on.
I've always found a good mix of new talent, growing talent, and old hands to be the best teams. For best results have enough experienced people around that the younger people have a variety of options to choose from and be able to work with the mentors they get the most out of.
Thats pretty old school. Now it seems that its really all about the next two weeks, and not about building good teams.
Yes, they have a program for those who are college hires (hired straight from college). I was not a college hire: this is my second job, but my first job at a purely tech company. My first wasn't programming related but I managed to change that. However, at my current job, I'm treated like a college hire yet not included under the program we have, including the benefits it has.
> I usually grab a coworker
I can talk to my manager and other coworkers if I need to and they'll help with things, it's not that they're not available to help.
> (Yes, its politiking)
I don't think it's politiking, but socialization is somewhat difficult at my company. The next-youngest person on my team is just about twice my age, and they've already got their social networks set or are simply uninterested. I found it much easier at my previous company, where even though I was nervous as a fresh grad, people were willing to talk and take breaks. I haven't really found an "in" socially, although everyone is nice and polite.
If there is nothing formal at your current place, you can try the informal route. Ask a coworker to join you when you go for a coffee break, and informally chat about work. Ask a few questions to see how they respond. This process is slow, but personally I've had the most success with this approach. (Yes, its politiking)
In my opinion, formal mentorship programs are uncommon. Usually the senior devs are under pressure to ship and don't have the option to help the new people (junior or not).