Och, come on. As a lifelong (LIFELONG!) football fan, I feel best placed to answer this question.
Ignore yon Spurs fan (Ricard), you've chosen (in my non-partisan opinion) a fine team to follow. Your manager might be a bit of a twat but Arsenal have probably been the most important team in revolutionising english football in the last 15 years or so.
As a quick aside I should point out that my football supporting is based on my childhood living in Perth in Scotland, where I was born. I used to go every saturday afternoon to catch St Johnstone, the local team, playing in the Scottish premier league. We had a few ups and a LOT of downs (football in europe is a LOT more hierarchical than any american sport; teams with tradition, like Manchester United or Liverpool in england, Rangers and Celtic in Scotand and Barcelona or REAL Madrid in spain tend to dominate for decades, even centuries), and I was there for every moment. There's local pride and passion in supporting your own team, even more if the guys that play are "normal" folks who you see week in week out in your local pubs and clubs. When your friends follow a local team, or even are "glory supporters" who follow a big team in the country and who gloat when they (almost inevtiably) beat you with their multi-million pound playing staff, there's one thing that makes you more happy than nirvana - kicking their fat millionaire arses off the park and giving them a good stuffing. One of the happiest moments in my life was standing on the terraces at McDiarmid Park and watching us hammer Dundee 7-1 a few years back - for other people, a completely meaningless match, for one or two people who were there, a definining moment in sports....
ANYHOW.... ACTUAL CONTENT STARTS HERE.....
I'm a big footy fan south of the border too and have been watching the season this year with great interest. A Lot of footie fans in england have been spewing bile about the fact that football is shit this time around because of abramovich and chelsea... I say that's a load of BS, this is the best season we've had in YEARS. So what if chelsea are going to win the league by a mile it's FANTASTIC we've got so many supposed tiny teams kicking the living shit out of the big boys. I've laughed like a drain every time i've watched wigan this year knock stuffing out of pumped-up prima donnas like the bucnh of foreign wasters at Aston Villa and Middlesbrough. Funny stuff to see a bunch of players on 40% of everyone else's salary give them a drubbing week in, week out and play good football whilst doing it. Same's true of West Ham, some truly superb players there (get Reo Coker in the england team in the nest 3 years I say, if Carrick don't make it!).
Anyhow, as to Arsenal. A good side but, I guess, not a truly "english" one. In fact, the most continental side in this country, mostly due to the influence of manager Arsene Wenger, a French transfer genius who's managed to stack up titles for fun in the last 5 years (3 of them) plus lots of other domestic silverware thanks to a very impressive couple of sigings that rank among the greatest ever in the history of english football IMO. He bought Thierry Henry for something like 3.5 million pounds about 7 years back (FYI, very little money at alll, compared to what chelsea pay for players), and moved him from a winger (player who attacks close to the side lines of the pitch) to an out-and-out striker (player who attacks down the centre), and watched him become the most sensational player on the planet in the last 5 years or so, as far as i'm concerned. The man is a genius, pace, skill, finishing ability, class, and, seemingly, quite a nice bloke too (oddly enough). he also rescued a guy called Patrick Viera from AC Milan about ten years back (a little known french midfielder) who became probably the best defensive midfield player in the world. Along with a number of other players, these guys made Arsenal the most successful team in the 21st century in england, though they won nothing in europe. Then, unfortunately, along came Abramovich.
Right now in english football, chelsea pwn everybody because they have more money (Russian billionaire abramovich has tumbled about 200m of his own money in in the last two years, and there's no transfer or salary cap in football) and have the best manager (sorry to Alex Ferguson, Arsene Wenger - "The Special One" has built a team pretty impressively - whine about the money he's spent all you like but Terry, Lampard, and especially Cole have become world beaters UNDER his managership; he's built a fine coaching staff too, as far as I can tell). Manchester United are the second best team, the Glazers (of Tampa sports fame) are the owners there, following a bitter (meaning - riots with molotovs, no joke) protest by the fans, who like to be "majority shareholders" in their own team and are too thick to realise someone else was owning them beforehand (duh.... what does PLC mean, mummy???). The tight pursestrings, however, mean that they need to get the very best out of the young players they have to potentially cope with chelsea's monetary hegemony in the next 5 years (Wayne Rooney, the young Man U striker, could, COULD, be the best player in this year's world cup, if everything goes according to plan for england, he's a SENSATIONAL 20-year old who Man U paid an astronomical amount of money to obtain when he was 18). They've gone (sensibly|) for the buy-young approach, because they know that they're not top-dogs anymore and chelsea have more money.
Arsenal and Liverpool, I'd say, are vying for 3rd and 4th places. Arsenal were THE champagen team a year or two back, built on (in the early 90s) a tough and (I though slightly overrated) english defence, "One nil to the arsenal" became a Highbury chant (until it became a painful overpriced excuse for a visit to your local library), or alternaively "boring, boring Arsenal". When Wenger came in, players like Henry (astonishing) Pires (getting on but still superb, French winger), Bergkamp (old as houses but amazing on a football, perhaps the best last-third passer in england, and, wierdly enough, scared of flying), Ljungberg (Swedish pretty-boy who did lots of nudey shoots for womens magazines) and Sol Campbell (English hard case central defender, extremely good at putting in muscular challenges and using his elbows in your cheekbones whilst heading the ball clear of defence) made them practically unbeatable and 2 years back they set the record for an unbeaten run in english football and, Chicago-Bulls-like, RAN AWAY with the premiership. Rather like Man U, they've learnt they can't compete with the big money (they never could; Wenger made them supreme with a combo of terrific coaching and superb buys, and then when he actually had money to spend he fluffed it on goons like Jose Antonio Reyes, not bad but NOT worth 18 million....), and they've started to buy cheap young players, especially from africa and france, in an effort (I think) to build a team for 2010-ish and try to vaguely compete in the mean time.
Problem right now with arsenal is a) they're young and b) they've got no experience and muscle. When they meet teams like Everton, Bolton and Charlton who chase the ball around and put in hard tackles, they're lacking the beef and the hard-headidness to compete. When Viera was there and Campbell was fully fit, they'd put in more than their fair share but now more often than not their midfield is full of skillful but inexperienced european players who aren't used to being rushed in possession and who make bad mistakes when that happens. Fabregas would be a good example.
As Ricard so succintly put it, if you're an Arsenal fan, you can't be too keen on Spurs. North London, Highbury (arsenal ground, they're leaving this year to move to a dull pointless-o-dome near Kings Cross Station, boooo! Although, now I think about it, Highbury was quiet as shit anyhow....), and White Hart Lane (spur's ground) are less than 5 miles apart. That's the sort of local rivalry you don't get in american sports. There are 20 league teams in london, 6 of them in the Premiership (top league) and many of them have old and long-held rivalries.
I reckon proper arsenal fans are serious supporters and well worth their weight in gold, they're serious fans, they love their team and they're certainly not fair weather fans. However, "Highbury" isn't just known as "the library" for hillarious rhyming-slang reasons. They're not the most vociferously supported team, and have become (at least in the last 10 years) a club with a variety of salt-of-the-earth fans (a lot of london cabbies - i.e. taxi drivers) and a lot of quite posh london folks too . If you want a successful team who are supported by a never-say-die bunch, well, it's tough. As an english non-partizan (i.e. I support a scottish club), I've got to say, the fans in England who'll die for their club tend to be in the north of england. The most famous clubs in this region are Liverpool, Manchester United, Manchester City, Everton, Newcastle and Leeds United.
Leeds have, unfortunately, died, due to mismanagement (they're in the Championship, effectively outside the top division of english football, due to the financial fuck-ups of a select few who would now be basically lynched if they showed their faces in leeds...).... Manchester United have a fan base worldwide, but, ahhh, that makes you a face in the crowd and it's boring as hell. Plus, if you turn up at ANY game in england and say you're a Man U fan you'll be laughed out of town (Yankees style) unless it's at Old Trafford. Everton are an admirable club with a fine reputation, and I LOVE their style of play now (no money, no compromises, hard as nails, but not very pretty.... OK, I grew up watching shit scottish football, ad David Moyes when he was a player at Dunfermline....Now the manager at Everton, and very successful too), but not very watchable. Newcastle have THE BEST set of fans in England (or close to it) and a couple of alltime great english strikers (Alan Shearer - in international football, 30-odd goals for england, Michael Owen, has just broken that record - I think they're 3rd and 4th in the all-time english goalscorer list) but too many injury worries and a wanker managing them. Ugly part of england but if you want ATMOSPHERE go to St James's Park..... I'm tellling you, Geordies know how to fucking CHEER. Compare to highbury....
The team I'd support out of all this nonsense is Liverpool..... Personally, they don't do much for me, but they play nice football (thanks to manager rafael benitez from porugal) and are the current reigning EUROPEAN champions, due to a pretty incredible run last year (think, erm, the Bears winning the superbowl or something - they are NOT the best team in europe!!!), and the greatest match i've ever seen in the final - 3-0 down at half time to the best defensive team in europe (AC Milan) and, lead by captain steven gerrard, they made it 3-3 and then won on a penalty shootout. The single best match i've seen in 15 years of watching live footy. Pure hollywood. Oh, and they've done ok this year (3rd in the league) without a lot of stars. Home town hero Robbie Fowler (who played for my home town team, leeds united) just re-joined after years in the wilderness. If you want to go to any one ground in england to experience a proper football atmosphere, it's Anfield. It's spine-tingling (I point out again I'm not a liverpool fan, far from it), even compared to Newcastle or Manchester United (been to both), and a chorus of "you'll never walk alone" is still THE thing to experience in english football IMO.
If you want to know any specifics let us know! I'll be willing to bet there's a lot of football fans on this forum. I love american sports (went to a few MBL games when I was over in 2003) but nothing beats the atmosphere of a proper football game. Soccer

. Anyhow, i'm afraid to say if you want to support a winner, it's got to be chelsea, but no-one can support chelsea right now

even if they are playing great stuff, nah, only kidding, they're a terrific side, and lots of admirable players IMO..... Choose one of the big teams, or better yet, a little 'un. There's 4 premiership ones to chose withing 80 miles of my house!
Monk