Hi.  I've been lurking around here a while, mostly playing Regulus, and wanted to share my primary build.  It shares a fair bit in common with other builds out there but tries to make the best of Reg's different skill strengths, at different stages of the battle.

A lot has been said about Regulus being either a sniper or a miner or a dps monster, but I believe he can be all of these, it is just a case of at what stage in the game each role is most effective.  Here is the base build:

1 - Angelic Fury 1

2 - Snipe 1

3 - Sniper Scope 1

4 - Snipe 2

5 - Explosive Mines 1

6 - Explosive Mines 2

7 - Explosive Mines 3

8 - Angelic Fury 2

9 - Mark of the Betrayer 1

10 - Mark of the Betrayer 2

11 - Shrapnel Mine

12 - Angelic Fury 3

13 - Angelic Fury 4

14 - Sniper Scope 2

15 - Mark of the Betrayer 3

16 - Sniper Scope 3

17 - Enhanced Attributes 1

18 - Enhanced Attributes 2

19 - Enhanced Attributes 3

20 - Enhanced Attributes 4

First thing to pick up is always AF, as it gives you splash damage which is crucial to take down early creep waves rapidly.  Generally I keep AF on all the time and use the Blade of the Serpent to top up mana when running low.  This combination can be an incredibly effective way to replenish mana while in combat, allowing you to spam other abilities.  Sniper scope 1 is also essential in levels 1-3 for out-ranging towers.

Early game, snipes can be extremely effective (and annoying), but by late game, the 1000 or so that a fully maxed full range snipe does just doesn't cut it.  Often demigods run well above that, or they have heals, HoL etc that can get their health up above snipe range.  Generally you will be lucky to get snipe kills after levels 10-12, and it becomes more of a harassing tool.  Therefore I go early game snipe, but don't take more than two levels.  If you are observant, this should get you a good few kills through the early-mid game.  I don't generally go for the tracking bug, and tend to use snipe opportunistically on demigods I have been engaging or that are elsewhere on the map, but if you want it, you could leave the second level of angelic fury for later and add it around level 7 or 8.  The one thing about regulus is that it is important to try and get some early game kills with snipe to give you a bit of an advantage, and to get the gold to get you out of his initial squishy state.  This should transfer to a solid advantage later on when you have more staying power.

While snipe is the ultimate early game harrassment/death dealing tool, mid-game is where mines and MotB come into their own.  Mines are brilliant for taking out creep waves and laying waste to demigods (or at least severely injuring them).  See Vid-szhite's mine build for some great mine tactics to infuriate enemies.  The point here is to get up to 3 mines as quickly as possible, as this increases the blast radius and will do  the most damage to creep waves and demigods.  If you have mines 3 by level 7 or 8, you can rinse creep waves in no time, racking up fast xp and gold. Hitting demigods with Motb, waiting for them to acitivate it and then hurling some mines at them while slowed can also create some very effective burst dps.  This is especially effective with MotB 2/3 and shrapnel mines, as the slows stack and you can follow up with heavy auto-attack and if necessary a snipe to get the kill.  

Late game regulus is all about massive dps.  Pumping up AF and getting some nice +attack items like the gloves of fell-darkur or slayer wraps and critically the mageslayer are what turns Reg into a dps monster.  You take to your wings of death, throw down MotB and when it pops, follow up with mines and autoattack.  Often I find that once his dps is in the 400+ range and he has decent lifesteal he becomes almost unstoppable, and will take down anything in his way in a matter of seconds.  And with increased range from snipers scope later on, if you make a forward 60 degree arc of mines (two sets side by side) anything coming towards you will get slowed and then hammered by your bow shots.   Final levels i normally just increase attributes.  Maim could also be useful, but by then you are normally into full-on assault mode, and there isn't a whole lot of chasing and kiting going on.  You are taking down towers/fortresses/citadels and any demigod that comes in your way, and extra hp/armour and attack speed all come in useful.

Items

First and foremost, Blade of the Serpent is your best favour item by a long way (although some could also argue for swift anklet in more of a kiting/opportunistic role).  BotS gives you a nice +25 attack, 400 mana, and allows you to gain 75% of your damage back in mana on every hit for 10 seconds.  Now what's not to like??? AF provides a constant mana drain, but it is worth it, and BotS will normally refill your mana bar in a few shots into a creep wave or tower.  It should be noted though, that you'll get much faster regen from creep waves first (because of splash, which in included in the regen), then towers, then demigods.  Because of armour, you will do the least damage per shot to demigods, and hence get the least mana back per shot.  Also its worth noting that unlike torchbearer, Regulus' abilities don't appear to confer mana back to you through BotS (at least mines don't).  So don't mine creep waves if you want to use them for a mana recharge!

As for items, normally i generally go for this order:

First, Banded armour + Gauntlets of Brutality, or alternatively drop the gauntlets for a combat pot and a teleport scroll, for a bit more staying power.  This is often preferable to the extra dps as reg is so squishy early on that that health pot may come in real handy.

This means that at level 1, Reg is 1820 health, 1284 mana, which is still squishy, but a little less than normal.  DPS is solid, at 173-185 (or 198-205 with gloves).

Then go for +speed items: boots of speed + wand of speed gives you a nice speed burst to get out of tricky situations and lets you get into and out of the battlefield more quickly.  They can also be used to chase for kills, but early game getting anywhere near the enemy towers is a bad idea and its a much better plan to go for the snipe.

After this, I get nimoth chest armour and the plenor battlecrown.  The Nimoth armour will give you a vital armour boost as well as more health.  Reg needs to get out of his uber squishy state ASAP.  The plenor crown is preferable to the Vlemish as we are more concerned about max mana than regen as we use BotS for regen primarily.

Once I have these, I normally go either for HoL or straight for Mageslayer.  Getting Mageslayer early is a huge advantage as it ups your attack rate signifciantly and gives you lifesteal.  If you combine this lifesteal with Narmoth's ring, you may not even need the HoL. (you could buy the HoL and then sell it for mageslayer too, the problem is i never do cause I like it too much)

Rounding out the late/endgame items, either the Cloak of flame or the Orb of veiled storms pushes your auto attack to extreme levels, and should give you a solid late-game advantage.  The Cloak is nice as it effectively replaces the plenor battlecrown for mana requirements, freeing up another equipment slot.  However, be careful about filling all of your pot/scroll slots.  You always want to hang on to some teleport scrolls to get you in/out of battle.  Increasing Health/Armour is also a priority.  And finally, what Regulus build would forget Ashkandor, which can either replace or combine incredibly well with Mageslayer.

Equipment

1. Banded Armour -> Narmoth's Ring

2. Gloves of Brutality -> Mageslayer 

3. Boots of speed -> Gloves of Fell-Darkur/Slayer's Wraps

4. Nimoth chest armour -> Groffling Warplate/Godplate

5. Plenor battlecrown -> Ashkandor (after Cloak of Flames)

Charged items.

1. Wand of speed

2. HoL

3. Cloak of Flames/Orb of veiled storms

Having a look at this, it looks like an extremely gold intensive build.  Regulus needs good items to make him effective mid-late game, but don't forget the citadel.  If you have got a few kills early, make sure you buy the gold and tower upgrades.  If you are pawning later on but haven't got giants out yet, sell some of your kit to upgrade creeps.  You can always buy it back, you know.  And don't forget to support your allies, if you don't they won't support you, and if that's the case, ol' Regulus will get squished mighty quick!!!