twitter bought its logo for hella cheap, but go find an online graphical design community. Most of them are looking for any type of work to add to their portfolio and most will do it for free or on the cheap.
Instead of putting up $300 on 99 design have a look around for a designer that makes logos that you like the look of and send them an email and ask what they can do for that amount. You might only get a few hours of their time, but you're probably going to get a much better result, and you'll be doing the whole design community a favour by not asking for free work.
EDIT: As a stop-gap, the inkscape option that pwim suggested sounds good.
This is a free market. Supply and demand. If people are willing to do quality work for free, let them. If someone is looking for quality work and they find it for free, they should take it. Doing a group of professionals "a favour" does not enter into the equation.
"If someone came to this community and asked to build them an app for free they would get shut down."
That's because no one made millions because of a logo. Apps are simply more valuable than logos, period. And they require more skill to create.
It isn't too hard to make an app generator that pumps up generic apps in a similar way that icons can be made by slightly tweaking another preexisting icon.
The value with apps is much the same as it is with icons (or design, in general); in how unique and well thought out it is, how well it applies to what you need it for.
As for your second point, how much would you say the brand equity of Apple, Coca-Cola, or Nike is worth? They would simply be selling electronics, sugary water, and shoes if they didn't have design and marketing experts building and executing their brand (experts who I'm sure have been compensated quite handsomely). While I'll agree that it's easier to "throw together" a logo than a web app, good design does require reasonable skill, training, and experience.
ADDED: I guess I should be clear that I'm rebutting the assertion that design is necessarily less valuable than software development, not that startups require Fortune 500 branding.
The brands you mention are priceless, but the logo is not. Nike's logo was cheap as hell, for instance.
99Designs serves a completely different market, and I think the "How much is a F500 Company's brand worth?" argument HEAVILY confuses marketing, design, branding and advertising.
The comparison to Apple, Coke and Nike isn't applicable. You're describing a different product than most startups are looking for.
Exhibit A: http://techcrunch.com/2006/07/15/is-twttr-interesting/
Exhibit B: http://en.wikipedia.org/wiki/Google_logo
http://www.dotweekly.com/the-story-behind-the-godaddy-name-a...
The last time I checked, Fortune 500 companies weren't shopping for logos on 99designs.
"They would simply be selling electronics, sugary water, and shoes if they didn't have design and marketing experts building and executing their brand"
We're talking about logo design for startups, not marketing strategy for large retail corporations. Apples and oranges.
"good design does require reasonable skill, training, and experience."
I absolutely agree. It takes a lot of skill to be a good designer.
It's possible to have a very successful web app with no professional design. Look at Craigslist.
It is impossible to have a successful web app that consists only of design and not the underlying code. I'm not saying that design is unimportant, or that it can't make or break a product, but you can't with a straight face make the assertion that it's as important as the product. It's the icing, not the cake.
Your logo is the single most important part of your brand and it drives the graphic design of the rest of you website. It is true that anyone with a little time can create a logo by choosing a typeface adding some colour and a drop shadow but making a logo that tells you something and holds a message is much much harder. I would be tempted to say that logo design is probably the hardest aspect of graphic design to master. For an example of a very clever logo that hold a hidden message take a look at the FedEx logo, see if you can spot the hidden image. Designing both a logo and a webapp are about knowing the audience and what makes them tick.
With that said something like 99 designs is actually a good way to get a first logo for your webapp. You can always iterate on the logo when you know the market is ready for your app, just don't underestimate it's importance.
The best comparison might be a white plastic yard chair and a vintage leather Eames recliner with matching ottoman. You can sit on both chairs.
With the current economic climate today I think there are a lot of unemployed artists, especially the newly graduated who at the moment maybe at a dead end job, but would be willing to design a logo for the experience. I've gotten free work from artist many times. I am well connected so they may do it for me for a future gain, which I don't mind.
Furthermore, the strength of a brand and logo is dependent on how well you execute and meet the expectations of the customer. Nike, coke, etc are well know because they offer satisfying products that meets or exceeds the customers expectations. Kotler and Jagdesh Sheth both teach this. You can have the coolest logo in the world but your app, for example, sucks shit your logo means shit.
/sarcasm