I'm just starting to plan a trip to the BI and at this point I'm traveling solo. Can anyone recommend reputable tour companies? I'd really rather not rent a car but realize that there are some places I probably won't be able to get to unless there's a good tour. I'm assuming that taxis and/or bus service is available in most areas.

Any info is appreciated.

I went on a Mauna Kea tour with Arnott's lodge out of Hilo. They also do a Volcano tour and a Waterfalls/Waipio tour. They are all discounted if you stay there and they also provide airport pickup. However, it's a hostel that also has private and semi-private rooms, so I don't know what you are looking for. But it's probably a good place to meet people to travel with also.
www.arnottslodge.com

Bus service is VERY limited and distances are big on the island so taxi's are going to be expensive.

The island is 200 by 200 miles, so a cab would be horribly expensive. The Big Island does have a bus system which circles the entire island, search the web for "Hele-On" for more info.

If you're staying in Kona, Waikoloa or Hilo there are some great tour companies who have pickups from those areas. Arnott's tour of Mauna Kea is wonderful, as is Pat Wright's tour (http://www.maunakea.com). Arnott picks up from Hilo while Wright's tour picks up from both Waikoloa and Kona. There are also horseback riding tours to Parker Ranch, Waipio Valley and tours to both the north and south coasts of the island. Pickup points vary depending on the tour company.

Funny, I was about to suggest Arnott's Lodge - guess it's unanimous!

When I went to the Big Island a few years ago I took a Roberts Hawaii Grand Circle Island Tour. I highly recommend it. Ask your hotel about, they should have information. They make pick-ups at all the major hotels.