Also, if you're generating a bunch of good code and solving hard problems, people are going to notice you.
If you're working for a small company where the CEO sifts through source control to see what's changing, producing good code will certainly suffice, but if you work in a large company with a multi-tiered management structure, keeping quiet only pushes the responsibility to promote your work to someone else - and you can't always rely on that happening.
In the cases where you can't rely on that happening, then that means no one else gives a damn about what you are doing. This would be very odd in a multi-tiered organization, since often times development projects are decreed onto the programming staff by strategic direction committees. If no one cares, the project is make-work; warning. Either it is going to contribute next to no value to the organization, or no one has a clue what value it is going to contribute. Either way, you'll be hard pressed to convince everyone who needs to be convinced what you are doing is that valuable.
To borrow a PG idea, to everyone above you in the management hierarchy, you are represented -- as an aggregate of the rest of your group -- by either your lead or manager. A lot of the interaction between your group and the rest of the company will be done by them. They need to be your advocate; if they're not doing that, then your entire group is getting shafted, and need to find a better advocate.
What matters is the value that your work delivers to the business. If you write software that consistently delivers value and has significantly positive impact, it should speak for you. If you work on unimportant projects with little or no benefit or impact to the company, it will not help you, and you should also wonder why you're wasting your time on it anyways. Certainly when it comes time for the business to execute cost-cutting measures like in times like these, they will wonder why.
Then there's politics which can render all of the above moot. It's unfortunate, but that's how humanity rolls. If you work in a large company and wonder how some totally useless and unimportant projects that cost the business money hand over fist manage to survive even during tough times like these, well, now you know why.
On the other hand if your job is writing software for a widget company than it better be vital part of every widget. You don't want to be the guy that is made redundant because what they assumed was good work contributed nothing to the overall business.
A company managed this way is a company that will have little left but a sales and marketing force eventually, because the executive staff will have pruned everyone else as being redundant. Arguably, this could happen even in a shrinkwrapped software company, where the software isn't just a vital part of the business, it is the only part.
Hire someone incompetent, or see someone incompetent get hired above you, you may find you'll be made "redundant" even if you are the last developer hacking on the product. It is employment at the will of your employer, and nothing says they can't terminate you due to their own incompetence.