OK so I'm up to level 42 with my Sith Assassin and playing on a PvP server. I haven't been to the RvR planet Ilum as of yet, because I plan on hitting that in a big way once I get to 50 and there's little reason to go there beforehand. PvP kills reward you with nothing (yes you read that right) and the rewards from the Ilum RvR zone are related to level 50 gear, so I just don't see much point in missing out on XP gain.
Open world PvP has been limited. There isn't a great deal of cross over between Republic and Empire leveling areas, particularly in earlier levels and whilst it does mix things up a fair bit more later on, it still doesn't really explode into a PvPfest because of the zone instancing and heavy use of phasing. This is not necessarily a bad thing for the game, as we must remember that SWTOR is one of the most PvE centric games ever made and as such it does allow the game to focus on its goals. However if for some strange reason you were expecting PvP servers to see PvP kicking off everywhere, well.... you would be both delusional and disappointed. Of course it would be a lot better if there were some XP gain linked to PvP kills, hopefully that will get introduced, but I doubt it.
Warzones (scenarios, battlegrounds, whatever... instanced PvP things) are as previously reported solid, fun and well made, but are at the same time deeply flawed and essentially broken because Bioware opted to have no level bandings. This means you've got stat bolstered level 10+ players going up against level 50s, which simply doesn't work because stat bolstering does not take into account the wider range of abilities, players min-maxing stats and the huge impact talent specs have for the higher level players. As a result almost every warzone is hugely unbalanced in favour of whichever team has the most level 40+ players and I can only presume makes for a shitty experience for lower level players. Now we can sneer at the lowbies and act like epeen pricks or we can recognise that for a game (and it's PvP) to be successful it needs to be accessible and enjoyable for players straight away, otherwise you just lose players for no gain to anyone else.
Also the only warzone that ever pops is Huttball, which is kind of like Bloodbowl, I presume this is because my server doesn't have enough Republic players on it because in Huttball you can face teams from your own faction. Though having played the Republic side in beta I can understand why people might not want to play with the mew mew mew crybaby jedi and their dull arsed storylines. :P
So all told and as expected, the PvP has not been particularly inspiring, though I do have some hope for the RvR zone Ilum. Apparently the planet has the problem of players from each faction effectively taking turns to complete the campaign stuff, which is no shock as we saw this with WAR and people choosing the path of least resistance, but my lot and I won't be playing along with that, so it should be amusing on numerous fronts :)
As of yet nothing with SWTOR or other games has changed my mind from WAR, DAoC and EVE being the only serious RvR games. Until Planetside 2 comes out...