As with Stuart's Magic User, I'm asking everyone to chime in with what they'd do  with a 1st level rogue.  3.5 rules mostly from the core book, but if there's something particularly spiffy from one of the supplements feel free to use it.  Just let me know what book it's from so I can check it out.

Looking for something along the lines of Grey Mouser, but without the magic using aspect.  But if you want to go in a different direction and build a cat burglar or a con-man, feel free to do so.

(And my apologies in advance if making a spin-off thread of this sort isn't kosher around here.)

If you want to go close to Mouser, I'd pick up 2 levels of fighter within your first couple of levels to get all the martial weapons and get the free fighter feats.  
 
Combat wise, I'd go either archer or (being more like mouser) two weapon fighting. For the former definitely get point blank which  is needed for all the archer feats.  Point blank range also fits in nicely with sneak attack range - maxing your sneak attack opportunities are the key to doing decent damage.  
 
Max out the classic thief skills: move, hide, locks, traps, tumbling.  The last it good for getting into flank position.  If you have good charisma, you have the skill points to get social skills.

Ok, two points:

The first is that the strongest Rogue builds out there use two weapon fighting right now. Two weapon fighting gets you more attacks, which gets you more chances for sneak attack damage. Since you're normally getting sneak attack against flat-footed and flanked opponents, the to hit penalty isn't that bad.

The second is that most Rogue builds end up being "R16" builds - 16 levels of Rogue, 4 levels of a class with full BAB (usually Ranger for the free Two Weapon Fighting feats). This gets you four attacks by level 20. You don't even really need to look that far ahead to consider this option - you'd want to take the Ranger levels relatively early (I'd say around character levels 4 to 8 personally). Use the PHBII option to get rid of the animal companion and replace it with Distracting Attack - which lets you treat enemies as flatfooted if you score a hit on them.

Anyhow, that's all further on.

At 1st level, you want to prioritise your stats as follows: Dex, Int, Con, Cha/Wis, Str. Good Dex and Int are key for Rogues, while a shitty Strength score won't really hurt you in combat because of sneak attack.

Skillwise, there are two core Rogue skills - Move Silently and Hide. Max these out and keep them maxed. In fact, that's a general rule of your skills. Don't waste skill points getting one or two ranks in something - either max it out or ignore it. Pick your rogue's core competencies and stick to them. I'd suggest Climb, Disable Device, Open Lock and Tumble as four other skills you should give a close look at.

Feats:

Improved Initiative, at least in a core-only environment. There are two feats you really want more, but can't take yet - Weapon Finesse (Rogues have to be 3rd level for it) and Two-Weapon Fighting (which you should get for free from being a Ranger - don't pay for shit you can get for free). Being a human Rogue can suck because a lot of the good feats you want to invest in right away require BAB +1 or better, which you only get at 3rd level.

For a Mouser-like character, pick up a few levels of Swashbuckler from the Complete Warrior book. Also in the Complete Scoundrel, there's a  feat that lets you combine swashbuckler/rogue levels regarding sneak attack, so that does come in nicely. You'll get a free Weapon Finess feat, some bonus hit points and the ability to add your Int to damage.
You'll need three (IIRC) levels for that, the rest won't get you that much. So after that, stick with Rogue or consider going for the Duelist prestige class.

Other than that, there's nothing really tricky for the rogue. Two-weapon fighting would be quite good for a sneak-attacker and charming swashbuckler, so I'd pick that as soon as possible. Weapon Finess (if not going for the Swashbuckler) is probably quite nice, too. Although with enough attribute points, you might have enough Strength. Dump Wisdom.

With a human, you should have enough skill points. Bluff, Tumble, Jump, Climb seem essential, add Forgery for slight Cugel style and you might have to stack up on Search, Disable Device and Open Locks for the party's adventuring needs. Use Magic Device will be rather important at later levels, although you don't neccesarily have to buy ranks early on if you plan on spending all your new points at some later level increase.

There's a feat that allows you to get your sneak attack damage with critical hits, that seems to be rather useful later on.

Personally, for good old sword & sorcery fun I'd go for Improved Unarmed Strike, although that isn't quite the most effective try. If you're playing the right way, you'll end up naked on balconies or prisons quite often, though

As someone who has played several rogues, here's a pro-tip:

Pick up the Run feat.  It'll save your life.

People will mock you for your choice.  People will claim that it's a lame feat.

People will also glare at you when you're haul-assing away from danger faster than they are.

Dash isn't terrible. I'd go for it over run. You get the extra 5 feet of movement, which can be good for setting up flanks, but it's more versatile.

Find a big large barbarian fighter and befriend him.
Learn to incorporate his fighting style into your tactics.

Seconded. This is keeping with the model of the character, allows you to flank -- and serves as a straight man for your cons/jokes.
(Overall, the last issue is the most important. Don't choose a paladin.)

If I remember right, isn't there a combat use for Bluff that lets you treat an opponent who fails a Sense Motive check against your Bluff as flat-footed?

That's the basic "feint". It's BAB + Sense Motive though, so the other guy has some chance of actually succeeding. Waste of time normally, you've really got to get the Improved Feint feat to make it work. Then you can do the feint as a move action, allowing you to attack in the same round. Still no multiple attacks. The "Invisible Blade" prestige class makes it a bit nicer.

Generally flanking is preferable. A fighter-type as a partner is really great for a rogue. If you find yourself out on your own a lot, feinting might start to be useful.

Be sure to acquire a Potion of Shrinking for those subterranean anthro-rat battles.