Well, it depends a little bit on what you mean by "recently"; the British navy adopted a common uniform for sailors in 1857, with the U.S. navy adopting one in 1807. I posted a response here to a question about how the traditional "sailor suit" developed:

http://www.reddit.com/r/AskHistorians/comments/2pdr6j/how_did_the_sailor_suit_develop/

There's a nice conversation there between me and /u/davidaop, our pirate specialist, about ready-made clothing.

In terms of "why" they weren't issued uniforms, it's a bit of a tough question to answer and one that probably would result in speculation. Speaking for the British navy: Sailors were generally not under military discipline in the same way that soldiers were; most of them were employed only for the length of a voyage and paid off at the end of it. The navy had also grown by fits and starts out of the king or Parliament requisitioning merchant ships in time of war, so by the large expansion of the navy in the Dutch wars and later in the Napoleonic period, there was a bit of a tradition of sailors (and ships for that matter) coming to the Navy ad hoc.

But in any case, around 1700 or so we see records of "slops" contracts being issued to contractors for a particular type of clothing, though those were not uniform but issued from each ship's purser. The system was unsatisfactory as the contractors bore risk for the cost of the clothes without having any control of their storage, so the clothes issued would often be moldy, rat-eaten or both. In some areas, sailors would instead of slops be issued canvas or other cloth to make their own trousers and jackets; in either case, the value of the slops or cloth would be stopped out of their pay. That system persisted until at least 1758, when the Navy Board took over issuing slops at its own risk, which tended to help with the issue of quality control.

It's also worth mentioning here that there wasn't a standard uniform even for officers until around 1800 or so; Prince William Henry (the younger brother of King George III) was a noted disciplinarian who ordered his officers to wear blue and to wear "uniform coats or jackets" around 1788, but in that context "uniform" meant similar, rather than identical.

Anyhow, this is hopefully helpful. Please let me know if you have follow-up questions or comments.

Hi there, I'm posting this as another top level comment to make sure the OP, /u/Jimmypickles, sees it.

I had a comment in a PM that asked about the dating of what I had here -- specifically, it said:

About how the British Royal Navy adopted a uniform in 1857, however I was under the impression that naval uniforms were introduced by Samuel Pepys in the 17th Century?

From "The Knowledge Web: From Electronic Agents to Stonehenge and Back" by James Burke, p211:

By 1685 Pepys was secretary to the navy and responsible only to the king. Pepys’ reforms effectively founded he modern British navy and dealt with virtually every aspect of naval life on shore and at sea. He introduced formal training for officers, who would now be required to be able to navigate. Discipline, pay, pension and medical treatment were regulated. Uniforms and saluting were formalized.

Emphasis mine.

In response, I sent this:

Great question! Pepys seems to have standardized a blue coat and some badges of rank (a eupalet, or two eupalets for senior post-captains) for commissioned officers, but he didn't do anything similar for warrant officers or common seamen. The gentleman WOs (purser, surgeon, chaplain) got uniform coats and swords to wear in 1805 or so, and the other WOs got uniform coats around 1807. It was ordinary seamen whose uniforms were standardized in 1857.

Wanted to post it here in the interests of clarifying the thread.