So the answer is: yes, you can , if you really want to.
In practice, though, it makes made little sense.
The Maldives are explicitly set up to discourage independent travellers.
The only places you can go without a permit are the capital Male, which is pint-sized and notably lacking in all the things that make the Maldives great (white sand beaches, clear water, gorgeous coral, overwater bungalows etc); and the resort islands, which are for guests only.
For travelling anywhere else, you need an "Inter Atoll Travel Permit" (IATP), which is normally only issued if you have an invitation from somebody living on an outer island.
This means an independent traveller is effectively limited to doing one of two things: Fly to Male and stay only there.
Unless you're there for business, this hardly seems worth the expense.
Fly to Male and pay the rack rate directly at a resort island to stay there.
This is almost certainly more expensive than a package that combines the two.
2018 update :
Things have changed considerably since this answer was written.
IATPs have been abolished, so you're now free to travel about on your own, and guesthouses and small hotels have sprung up in response.
Here's a random blog entry with some pointers.
travel.stackexchange.com/users/1893/lambshaanxy
We went to the Maldives from Sweden this summer.
I checked out prices of regular flights and it was more expensive to just fly in then to buy a package from a tour operator so when it comes to the Maldives I would say that tour operators is the cheap option.
However - if you are nearby anyway (India?)
it may be different.
travel.stackexchange.com/users/384/froderik
The only way to fly there cheaper is to string separate flights together.
I.e. from Australia
it's possible to get there for just over £500 GBP return by flying: Melbourne→Malaysia •
Malaysia→Sri Lanka •
Sri Lanka→Male.
Obviously, this is going to be a headache, and the you have the hotel costs.
I'm sure the answer above is on the money.
So to speak.
travel.stackexchange.com/users/1544/Matt
Condor fly to Malé from Frankfurt (am Main) and has pretty decent rates.
So if you fly from Europe, then it's cheaper to get there than on most packages I've seen in catalogues.
Still, I would also like to ask the for your experience what to do next, when I get there.
travel.stackexchange.com/users/2513/Tschareck
I planned my trip to Sri Lanka without agencies.
I found tickets with Condor Airlines with 1 stop in the Maldives.
I have never been before at the Maldives, so I decided to stop for 5 days in Malé.
So I have 5 days to explore Maldives as an independent traveler.
I can tell you, that there is no problem for you to plan your trip to Maldives without agency, but it depends from "What you're really wanting from your trip?
" If you want to stay at Malé - it will cost for you not a big money.
But be patient!
Any your movement in the Maldives will cost for you huge of money.
For example: One way trip from Malé to the nearest island will cost for you $500 minimum (for 1 person).
So I recommend to plan this trip by yourself if only Maldives is not your final destination.
But if you need to relax, I think it will be better to get tour package.
If you need more information, You can read an article at my blog Real Truth About Maldives Capital (Malé) .
If this information will useful for you, please leave a comment!
travel.stackexchange.com/users/6272/Alex Cardo
Organizing your travel without agents is almost always cheaper and more fun.But does that also apply for Maldives? Can I just travel to the Maldives? Do you have some tips or experiences to report?
Can you go to the Maldives without assistance of a travel agency?
travel.stackexchange.com
<budget><planning><travel-agents><maldives>
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travel.stackexchange.com/users/109/realbot
You can go without a travel agency if you really want to, but you will need to string separate flights together to make it cheaper. it is possibile to travel to the Maldive without going though a travel agency and  If you take an indirect flight it will be cheaper.
You can travel to the Maldives without a travel agency but your flight will only be cheaper if it is indirect. 