Travelling on your own has all sorts of advantages, as well as a few disadvantages, to travelling with a companion...
I assume you are travelling for pleasure and not business...
When i travel i usually either use couchsurfing or stay at hostels... Not only are they both cheaper than staying in expensive hotel rooms that i usually only ever use to sleep in (rest of the time i am exploring out and about full bore) but they also provide interaction rather than being stuck up in a hotel room on your own which can be the pits, only surpassed by being with an inconsiderate friend/partner or if you have had a bit of a barney and the trip isn't going so great...
With the hostel you obviously bump into room mates who usually are happy to help each other out but can also bump into people from all over the world down in the eating/bar/pool area and can also makes friends as well as find companions to go out on day trips or explore the city... In NYC me and my NZ friend i was travelling with bumped into a Swiss young guy and a middle age Aussie over a couple of days and ended up going to a baseball match together... There is obviously the room mates from hell which i have copped as well but they make a very small percentage of the people that I have bumped into/roomed with...
Couch surfing is different but another option, although often easier to find potential hosts in autumn/winter of locations you are going to rather than spring/summer when, especially in the most popular cities, hosts are getting deluged with requests... But I've had some good experiences there as well... I have also hosted couch surfers here in Perth and took one of them to King's Park with a few beers one Friday arvo to look over the city and chill out... Couch surfers have taken me to several dinners/parties with friends, out to a movie and I went to band jam session with one in Athens (but couldn't summon the courage to join in the singing) so couch surfing is definitely something i recommend if travelling on your own...
Another way if not actually staying with a host is to join couch surfing and then join a group for a city your visiting. Not only can you ask lots of questions and get advice, but in Rome i noticed there was going to be a roof top party one Saturday night, I asked if i could join in and ended up paying 5 euros to be be on the roof of a 6 story building with amazing views including clear views down to the big wedding cake Vittoriano monument, tunes playing, drinks and food etc (i drank maybe a little too much perhaps) but again, locals and travellers from all over the world having fun and meeting each other... I bumped into and talked with an Iranian medical student and a German guy who worked for the European Space Agency?!?!? I also went to a bar in Amsterdam one Friday night for a Couchsurfing get together of locals and visitors... Travelling alone these types of get togethers would definitely be my preference to heading out to bars/nightclubs on my own!!
I think as a girl it is probably easier to generate a conversation if you want one, although probably also easier to generate unwelcome attention... But i have run into many single females at places i've stayed who seem to be having a great time, teaming up with other females or guys or groups, I think its the mind set you bring with you and what you open yourself up to experience rather than expecting problems/the bad and you will find it... Group walking tours are another good way to get out and about and maybe also bump into people in the same situation and they can be free in a number of cities throughout Europe...
With planes, I have struck up one or two interesting conversations with people next to me, but most of the time just have earphones in listening to movies/music and don't get bothered other than a few pleasantries... I wouldn't stress ahead of that for the remote chance that someone will really be a pain.. Stick the headphones in and they soon get the message...
