The term "founder" describes your relationship to the history of the business. Page and Brin will always be Google's founders. The term "CEO" is about your position in the current organization's hierarchy. Some founders will be CEOs, at least for a while.
Titles are the easy way for outsiders to understand how to connect with your organization. So if you're the head, just use the title CEO unless you have some strong reason not to. That way people will know to come to you with CEO-ish things. There's no harm in putting "founder" on your business cards as well. E.g., "Founder / CEO" or "CEO & Founder". But things like "CTO & Founder" are also legitimate, so don't go with "Founder" alone, or people will be left wondering which things they should contact you directly about.
The previous answers given here are great, but I've copied a trick from legendary investor Monish Pabrai that I've used in previous startups that seems to work wonders -- especially if your company does direct B2B sales.
Many Founders/ CEOs are hung up on having the Founder/ CEO/ President title. As others have mentioned, those titles have become somewhat devalued in today's world -- especially if you are in a sales meeting with a large organization. Many purchasing agents at large organizations are bombarded by Founders/ CEOs/ Presidents visiting them all day.
This conveys the image that a) your company is relatively small (the CEO of GM never personally sells you a car) and b) you are probably the most knowledgeable person in the organization about your product, but once you land the account the client company will mostly be dealing with newly hired second level staff.
Monish recommends that Founder/ CEOs hand out a business card that has the title "Head of Sales" or "VP of Sales". By working in the Head of Sales role, and by your ability to speak knowledgeably about the product, you will convey the message that a) every person in the organization is very knowledgeable about the ins and outs of the product (even the sales guys) and b) you will personally be available to answer the client's questions over the long run.
I've used this effectively many times myself.
I work with many CEOs and C suite executives as well as "startup CEO" I gotta tell you that the CEO term in our world is becoming less impressive and more egotistical. Most founders want that CEO but aren't really worthy of a CEO title. Just because you launch doesn't mean you should lead much less that you are capable of long term thinking.
Consider Steve jobs who went through this and then had to prove himself to be worthy of such role. If you go with a lesser egotistical title, like cofounder & (___) fill in blank with something you are really useful at.. You can come across as more of a team player, focused in your and your company's efforts... Etc.
I own a web design firm, I call myself owner.
I own and run a hosting and technology it company, I call myself cofounder and chief strategist (not CEO)
I co-own a multistate cleaning company and call myself co-founder and lead marketer.
I had other startups and did also call myself a CEO until I knew better. I read a lot on management, I give presentations for successful leading, team evangelism, gaining competitive advantages, host a series of coaching sessions every year, personally helped several now successful individuals in growing their companies. And even though i have an MBA and all this experience I know that if I applied for a CEO job somewhere I probably wouldn't still get that top role. You must earn it. CEOs has huge responsibilities.
Be a leader and know when you are and when you are not a true CEO or manager for that matter.
Read the Harvard MBA oath and read up on Henry Mintzberg on managing.
On top of what was discussed here, the most important message to convey via a practical title is:
a) did you started the company - e.g. Founder, Co-Founder
b) what's your key role (whom you make most of the decisions as) - e.g. CEO, COO, Business Development, Product, Marketing
There will be drawbacks when your audience are not sure what you do by reading your title, e.g. Chief Rainmaker, Chief Problem Solver... <- bad examples
You will always be a Founder or Co-Founder and your title will change. Be sure to be careful however how you dole out the Founder/Co-Founder titles. That should be a lifetime title so be sure it goes to the right people who played a major role in the starting of the company and who will continue to play a role in the years to come. Another option is to give yourself the title President if you have plans to find someone to run your business (say if you are a technical founder)
If you are opening a pizza restaurant, then go with Owner.
If you are starting a tech company that you want to grow into the millions in revenue, CEO/ Founder is fine (both).
There are people that think that a "CEO" title for a company with 2 people (for example) is egotistical and looks bad. So, they stick with Founder and other titles early on.
Although well placed (I thought that, too), I don't agree.
When I'm trying to talk to who represents a company (for investment or doing a business deal) I want to know who the CEO is so I can talk to them. I don't want to wade through a bunch of Founder titles, I want to know the designated point person for this business.
I mentor at University level for the Entrepreneurship program. I see this all the time!
Chances are as a new business you are "Jack (or Jill) of all trades", and are an expert at whatever your business does, and that is why you started the business.
BUT as a new business, you will NOT be doing the tasks of a "CEO". [Google: CEO job description]
Wait till you've moved to a place where you are just doing CEO work, or leave room for the business to grow and let some other C level experts come in.
NOTE: Read Micheal Gerber's "E Myth Revisited". This is the very best business book for Founders. You'll learn what is really required to intentionally create a business model that you can franchise/ sell/ or walk away from and let operate on it's own.