If your time permits, certainly. It's a good way to build chase experience during the less-interesting storm days and keep in tune with the weather during the off-season.
The startup costs can be a bit higher, since you'll need to buy at the very least a 2-meter transceiver and a good antenna; others may want a mobile setup for their vehicle. Costs can add up quick!
Of course you'll also need to get an amateur radio license. It's not as hard as it used to be decades ago, and you won't need to learn Morse code, but it will require some studying. A good book to get started with is Now You're Talking, which takes you step by step on how to get that license. Also you'll need to find out whether you have a local SKYWARN group that operates a RACES or ARES net when the weather gets bad. If you're out in a remote rural area, your options may boil down to using the phone to do any spotting.
Even if you don't have an amateur radio license, SKYWARN schools are held annually in many counties. It's a great place to meet other severe weather enthusiasts, learn about amateur radio, and brush up on visual identification techniques that are essential to any kind of chasing or spotting. For example, here is the North Texas SKYWARN school schedule.
Note that you may not have much independence and flexibility, as the net controller may direct spotters to take up a certain position. You may also be torn between going out chasing on your own and sticking with the net to help with local operations. Chasing is not the same as spotting! The responsibilities and priorities are much different.
Tim is right that spotting and chasing are drastically different. Local spotters are very helpful to NWS offices. Spotting rather than chasing is probably a lot safer if you are inexperienced too. If you are inexperienced and you go chasing you can put yourself in some very dangerous situations if you get so lucky as to hit the nail on the head and get a vigorous storm. I've known of experienced chasers who have had encounters too close for comfort.
If you want the experience of chasing without the risk of making uninformed decisions, you probably should consider a chasing tour.
Spotting is also a great way to get to know your local Emergency Management folks as well as the people at your area NWS offices! I've found that they are very receptive to your questions and discussions when they know you can make a positive contribution to their office.
That's how I got started, and that's how alot of people started I am sure.
A good place to look for ham clubs is www.arrl.org also the NWSFO sometimes will annouce on their webpages when the next skywarn training classes schedules are. They are usually in the spring and fall, at least in Georgia they were.
Another aspect to spotting is that many Emergency Management groups use public service frequencies in the 150-160 MHz range because most of their volunteers do not want to become hams or to invest in ham radios. They will take spotter reports on these frequencies and then have a ham relay the report to the NWS.
Some of the radios that operate on these frequencies cost more than ham radios because they have to meet a different technical standard for FCC approval. Many ham radios can be modified to work on non-ham bands, but that is illegal under FCC regulations. However, the FCC has not vigorously enforced this rule because most people that use mofified ham rigs for CEM work generally do not cause problems. If you find yourself in an Emergency Management group that uses the 150-160 MHz range, you have to evaluate for yourself the risk of using a modified ham rig. However, FCC rules also state that during emergencies (life-or-death situations) you may use any means of communications that works.
I am not endorsing or condemning the practice of using modified ham radios for use on non-ham bands. I just want to inform people of something they may encounter and to give them the information they need to make a decision on which radios to use.