On PS3 there is no hour counter like on steam, but there is a way to see how many hours you have played on a single character! This is what to do: PS3 xmb>game>Saved Date Utility (PS3tm)>hover over your latest Skyrim Save>It will come up with hours played!

It will come up like this: 000.000.000 (it will have numbers instead of zeroes).
The format is: hours.minutes.seconds.

If you want to check in game (thanks to michaelpk for this) do this: pause menu>save game>reopen pause menu>load>hover over your last save.

you can see it ingame too.

go to load or save then look under the image of the gamesave.

it is hours, minutes and seconds.

You have just made my life so much easier. I hated having to quit my game to check, thanks!

I'm going to edit that in now

If I remember correctly, I think the PS3 dosen't allow you to see the hours you've played in the conventional way xbox and PC users do. Might be wrong though.

Edit: never mind.

It only display the amount of hours you spent with that one character though, and it doesn't include the times you reloaded an earlier save because you died or whatever.

I've known about both ways for quite a long time. My first character had the highest amount of hours with 450 tucked under his belt.