Q:

Why did Rama construct bridge to Lanka?

Why did Rama construct bridge to Lanka and did not use boats or ships which were easy to build? Any reason that you can think or mentioned anywhere?

A:

Why option of crossing ocean by boats was not chosen?
I. Time Limit
Sita sent a message via Hanuman that Rama should arrive in Lanka within a month:

जीवितम् धारयिष्यामि मासम् दशरथ आत्मज || ५-६५-२४
ऊर्ध्वम् मासान् न जीवेयम् रक्षसाम् वशम् आगता |
"O Rama! I shall be sustaining my life for a month. Having come into
the control of demons, I cannot survive beyond one month."

II. Rama's Army was Huge

बलम् चाकाशमावृत्य सर्वतो दशयोजनम् |
तत्त्वभूतम् महारज क्षिप्रम् वेदितुमर्हसि || ६-२०-६
"O, monarch! Their army is employed around a radius of ten yojanas (eighty miles)on all sides. You have to ascertain this truth quickly"
तानि कोटि सहस्राणि वानराणाम् महाओजसाम् |
बध्नन्तः सागरे सेतुम् जग्मुः पारम् महाउदधेः || ६-२२-७७
Those thousand crores of monkeys in a great spectacle reached the
other shore of the great ocean soon after building that bridge across
the sea.

Boats and boatmen were not available in that big number hence constructing boats and arranging boatmen would have taken more time. Also, few Rakshasas used to live in water hence they could attack on boats. Defending on boats was bit difficult.
Then what alternate solution was chosen?
Rama requested Sea God to give him path so that his Army can reach in Lanka:

तस्य रामस्य सुप्तस्य कुश आस्तीर्णे मही तले |
नियमाद् अप्रमत्तस्य निशास् तिस्रो अतिचक्रमुः || ६-२१-१०
Following the scriptural injunction, that Rama who was devoted to his sacred vow, while sleeping on the ground spread with Kusha grass, spent a time of three nights there.

But,

न च दर्शयते मन्दस् तदा रामस्य सागरः |
प्रयतेन अपि रामेण यथा अर्हम् अभिपूजितः || ६-२१-१२
Though honored according to his worth by the self subdued Rama, the careless ocean did not appear in his personal form to Rama.

Then Rama became angry and uttered following words to Sea

शरनिर्दग्धतोयस्य परिशुष्कस्य सागर |
मया निहतसत्त्वस्य पांसुरुत्पद्यते महान् || ६-२२-२
मत्कार्मुकनिसृष्टेन शरवर्षेण सागर |
परम् तीरम् गमिष्यन्ति पद्भिरेव प्लवङ्गमाः || ६-२२-३
"O, Ocean! A vast stretch of sand will appear, when your water gets
consumed by my arrows; when you get dried up and the creatures
inhabiting you get destroyed by me."
"By a gush of arrows released by my bow, our monkeys can proceed to
the other shore even by foot; O, ocean!"

And when Rama was about to release Brahmastra, Sea God appeared and uttered these words:

अयम् सौम्य नलो नाम तनुजो विश्व कर्मणः |
पित्रा दत्त वरः श्रीमान् प्रतिमो विश्व कर्मणः || ६-२२-४४
एष सेतुम् महाउत्साहः करोतु मयि वानरः |
तम् अहम् धारयिष्यामि तथा हि एष यथा पिता || ६-२२-४५
"O, excellent man! This one, named Nala, a glorious person, is the son of Vishvakarma; who was given a boon by his father and is equal to Visvakarma."
"Let this greatly energetic monkey build a bridge across me. I can hold that bridge. He is just the same as his father."

And Rama accepted this proposal.
Other Related Posts:
Description of Ram Setu
Who are Nala and Nila in Ramayan?
What scriptures describe the origin of Arjuna's monkey flag?

A:

Well your question is a valid one but I am not sure if there are any scriptures (there maybe) that may point out in this direction, but there are few things that come to my mind when I think about it:

Ships and boats would have meant cutting of huge number of trees which is against the nature plus not expected from someone we see as an avataar of almighty. Stones were merely relocated from one place to another (land to sea here).
Since the army was huge one so they would have needed quite a lot of ships and boats and it would have taken more time than the stone bridge. Time was certainly a factor.
More of a permanent solution cause weather storms etc could have damaged or sunk some boats/ships hence the life of vanar sena would have been in danger.
With stone brigde your army can move along heavy loads as the bridge is constructed (like a human chain) where as in case of boats/ships it would have been small disjointed groups at a time hence more trouble.
Another fact could be that since the stone bridge was made using certain mantras hence it would have lasted long enough for army to retreat after the war, where as the ships/boats could have been burnt or drowned by the enemies. I thought about this because we still know that Rama Setu exists even today after millions of years where as we have heard about Pushpak Vimana (airplane) but don't have anything as a valid proof (same stands for boats/ships they would have been damaged by now).

The term Setu means a bridge, one that connects 2 disjointed entities for a specific purpose, where as a Kishti means a boat/ship that can float any where if not fixed to a permanent structure. 
Even if you analyze it in current scenario for instance the mumbai worli sea link (just an example), after it's construction not only time is saved but also more people can commute to & fro plus you can transport goods easily. Whereas using sea boats/ ships etc takes more time and can transport lesser number of people on daily basis.
Please feel free to agree or disagree :). 

A:

Thanks to @Just_Do_It and @YDS to providing answers and here are two cents from my side: 
while watching ramayana (TV series, based on ramcharitmanas and valmiki ramayan). Laxman suggested construction of boats but vibhishan suggested that sinking of boats is easier for lanka warriors (using big stones) so unsinkable medium of travel should be searched. No one knew what to do that's why he suggested to ask solution from ocean. 
Note: As my answer is based on TV series, I dont claim it to be 100% correct.

