This will be an incoherent rambling about supporting England, so bear with me!
I'm an England supporter. I've largely grown up down South, which may have something to do with it. I've been to numerous games at both the Old and New Wembley and a couple of away games. Travelling abroad with England opened my eyes to the culture of the fanbase, with neither trip an experience I really want to repeat. A mate and I went to Switzerland away in 2010 and the way England fans behave abroad is embarrassing. The songbook is horrific - a majority of the crowd sing Ten German Bombers, No Surrender etc no matter who the opponent. The other away I attended was Wales, and I was embarrassed to be in the England section. Every song was a generic, crap chant about sheep, how shit Cardiff was (this was around the time of the 'I want to go home' chant) etc. I understand this is the case at aways (we sing about Manchester at Old Trafford) but there was barely a song in support of the team, and bringing inflatable sheep to Cardiff and shouting sheep-shaggers isn't really my cup of tea.
The main problem with England's fanbase is that the 'hardcore' are the worst of the lot. Largely in club football, you'll get a lot of 'whoppers' at home games but not many at aways. The travelling fans generally know the score. This former is true of England, however the travelling fans seem to be the worst for hooliganism, xenophobia and other negative traits that have already been described on this thread.
I didn't miss an England game at the New Wembley for several years after it opened, and most supporters are either Soccer AM types or casually racist & xenophobic (or often both). There seems to be barely any what I would call 'decent' fans, i.e. those who don't boo the opposition anthem, sing 'who are ya' or about England's military and/or political history. I used to go to the games in spite of the fans, but have since preferred to save my money for other things, i.e. Liverpool aways or train fares to Anfield.
Outside of the support, a big problem with England is the lack of any meaningful matches outside tournaments. The qualifiers are almost always against piss poor opposition, with the games against decent sides often friendlies where both teams play their reserves. Whilst in the Premier League anyone can beat anyone, and every match counts, England could play San Marino 100 times and would always beat them at least 3-0. I actually enjoy going to the matches to see the team play, but I can see why there's no appetite to watch them, never mind that generally speaking international football is dull as dishwater!
I'm not sure if I understand people not supporting them because of the players. I found it strange supporting John Terry and Wayne Rooney, but I could bear it when they were wearing an England shirt. If we signed John Terry tomorrow would you not support us? I'm of a similar mindset with the fans - believe me nobody dislikes the stereotypical England fan as much as me, but England are still my team. Again (hypothetically) if Liverpool fans suddenly started behaving like England fans would you stop supporting us? To be fair I can see why these would be reasons not to bother if you've never followed England (it would certainly put me off), but if you would otherwise support England I'm not sure I get it myself.
On a separate note, and this is probably just me, but I can't stand the hype around major tournaments. At club level everyone hates bandwagon jumpers. The song 'where were you when you were shit' gets sung at Stamford Bridge and the Etihad regularly (although City's fanbase is still almost non-existent to be fair). With England it seems encouraged to not bother in the qualifiers but to turn up for tournaments. Perhaps this ties in with tournaments being the only important games in the international calendar, but personally I hate going to the pub and hearing people spout shite who haven't watched a game in two years.
All negativity aside I still support England, as I'm born and bred here. I'd definitely identify as British, and strangely wouldn't want to be labelled as an England 'fan' for all the connotations that come with it, but I still support the team. That being said, there's a part of me that would hate the hype if they actually won anything! Given that it's no surprise I'm still club over country by a long distance. I'd much rather Liverpool won the League Cup than England won the World Cup - to be honest if we were drawing 0-0 in injury time on the first day of the season and you offered me a Liverpool penalty or an England World Cup win I'd go with the former.
Long story short I hate everything about supporting England, and would much prefer success at Liverpool, but I still follow the national team because I've lived here my whole life and grown up supporting them. More fool me!