I usually travel solo and let me tell you it's the best way to do serious travel - as opposed to relax or party travel.
My tips:
Stay in backpackers hostels with high atmosphere ratings, common rooms, kitchens and meet other solo travellers. Avoid Hostelling International hostels unless you want to make friends with local school kids and young families - the only exception to this being the Iceland HI hostels, which are surprisinglyfun to stay at (they're also the only hostels in Iceland which helps their atmosphere rating a lot). Hostels that have bars or restaurants are great too.
It can be boring. Especially at night. I try to find events that are open at night and I'm keen in night photography.
Get an iPod touch or iPhone or some sort of palm device, load up the Stanza application (iPods) or get your hands on mobireader (for all other devices) and fill it up with ebooks - all free - or solitaire games or audiobooks. If you can handle the extra weight and deal with the associated security issues, you can take your laptop (I never do, they're just too bloody heavy and there's always the risk of them being stolen when you stay at hostels). Modern electronics are the solo backpackers friend for getting over boredom. Particularly if you seek out a hostel with wifi - in fact I'm spending a lazy night in Venice planning a trip to Spain.
You can also carry a pack of cards - UNO, anyone? - to sucker other solo travellers out of the solo-induced haze.
I'm very independent - I prefer to spend my day sightseeing or walking around alone (I get really irritated when I sight see with other people, generally). But I usually spend breakfast time (its good to go with hostels that include breakfast as its the main place youll socialise) and nights with other travellers, usually making 'single serve friends' in different places. A lot of people you meet you're never going to see again and chances are you're not going to have much uncommon with the people you do meet besides a love if travel. But you're going to meet some amazing people too, who you'll keep in contact with through facebook and one or two you're also probably going to make theeffort to go visit or they visit you sometime in the future (i did a USA trip just to see a former travel buddy as well as Europe.)
A tip that will help with cost is to get in on couch surfing - google it. I prefer hostels to couch surfing but when I go to really out of the way cities it's really nice to 'know' someone there.